Details

analyze772.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample62.0ms (0.1%)

Algorithm

1×

intervals

Results

14.0ms	177×	body	128	valid
9.0ms	36×	body	1024	valid
8.0ms	33×	body	1024	nan
5.0ms	24×	body	512	valid
3.0ms	19×	body	512	nan
3.0ms	50×	body	128	nan
2.0ms	17×	body	256	valid
1.0ms	2×	body	2048	valid
1.0ms	5×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify354.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

587×	`div-sub_binary64_83`
436×	`distribute-rgt-neg-in_binary64_36`
377×	`times-frac_binary64_84`
325×	`distribute-lft-neg-in_binary64_35`
254×	`distribute-neg-in_binary64_39`
245×	`associate-/l*_binary64_23`
211×	`associate-/r*_binary64_22`
205×	`distribute-neg-frac_binary64_42`
197×	`sub-neg_binary64_71`
179×	`distribute-rgt-in_binary64_28`
172×	`exp-prod_binary64_130`
154×	`associate--l+_binary64_15`
142×	`distribute-lft-in_binary64_27` `associate-r_binary64_18`
139×	`associate-l_binary64_19`
122×	`associate-/l/_binary64_25`
117×	`cancel-sign-sub-inv_binary64_44`
102×	`neg-mul-1_binary64_74`
95×	`distribute-frac-neg_binary64_41` `distribute-lft-neg-out_binary64_37`
92×	`associate-+l+_binary64_11` `associate-+r+_binary64_10`
91×	`neg-sub0_binary64_73` `unsub-neg_binary64_72`
86×	`distribute-rgt1-in_binary64_34`
78×	`*-commutative_binary64_9`
60×	`associate--r-_binary64_17`
45×	`associate-/r/_binary64_24`
42×	`-rgt-identity_binary64_68` `associate-r/_binary64_20`
39×	`distribute-rgt-neg-out_binary64_38`
37×	`associate-*l/_binary64_21`
33×	`*-lft-identity_binary64_67` `associate--r+_binary64_14` `+-commutative_binary64_8`
32×	`distribute-rgt-out_binary64_31`
29×	`associate--l-_binary64_16`
23×	`+-rgt-identity_binary64_63`
22×	`/-rgt-identity_binary64_69` `+-lft-identity_binary64_62`
21×	`associate-+l-_binary64_13`
20×	`swap-sqr_binary64_45`
19×	`mul0-lft_binary64_60` `associate-+r-_binary64_12`
18×	`mul0-rgt_binary64_61`
16×	`cancel-sign-sub_binary64_43`
14×	`sub0-neg_binary64_65` `remove-double-div_binary64_54`
11×	`remove-double-neg_binary64_66`
9×	`distribute-lft1-in_binary64_33` `distribute-rgt-out--_binary64_32`
7×	`--rgt-identity_binary64_64` `div0_binary64_59`
4×	`pow-plus_binary64_141` `div-exp_binary64_129` `exp-sum_binary64_124`
3×	`prod-exp_binary64_127` `exp-diff_binary64_126` `cube-unmult_binary64_115` `*-inverses_binary64_58` `pow-sqr_binary64_51` `count-2_binary64_26`
2×	`rec-exp_binary64_128` `unswap-sqr_binary64_46` `distribute-lft-out--_binary64_30` `distribute-lft-out_binary64_29`
1×	`exp-lft-sqr_binary64_133` `exp-sqrt_binary64_131` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-sqrt-square_binary64_91` `sqr-pow_binary64_50`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `log-div_binary64_165` `log-prod_binary64_164` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow3_binary64_144` `unpow2_binary64_143` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-mult_binary64_108` `cube-div_binary64_107` `cube-prod_binary64_106` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `distribute-neg-out_binary64_40`

Counts

1 → 4

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	45	41
2	99	41
3	194	41
4	414	41
5	895	41
6	2913	41

prune17.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1	3	4
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	4	5

Error

42.3b

Counts

5 → 4

Compiler

Compiled 216 to 145 computations (32.9% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 t (/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))) (sqrt.f64 2)))
0.3b	(/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))) (sqrt.f64 2))
9.7b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite1.1s (1.1%)

Algorithm

1×	rewrite-expression-head

Error

42.2b

Rules

300×	`times-frac_binary64_84`
189×	`sqrt-prod_binary64_94`
175×	`add-sqr-sqrt_binary64_100`
174×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
46×	`associate-/r*_binary64_22`
11×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
9×	`associate-/l*_binary64_23`
6×	`add-log-exp_binary64_117` `div-inv_binary64_75`
5×	`pow1_binary64_139`
4×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`flip3--_binary64_82` `flip--_binary64_53`
2×	`associate--l+_binary64_15` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `sub-neg_binary64_71` `cancel-sign-sub-inv_binary64_44` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `sqrt-undiv_binary64_99` `associate-/r/_binary64_24`

Counts

4 → 270

Calls

4 calls:

25.0ms	(/.f64 t (/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))) (sqrt.f64 2)))
17.0ms	(/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))) (sqrt.f64 2))
14.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
14.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))

Compiler

Compiled 15062 to 8778 computations (41.7% saved)

series9.2s (9.8%)

Error

6.1b

Counts

4 → 76

Calls

4 calls:

3.3s	(/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))) (sqrt.f64 2))
2.7s	(/.f64 t (/.f64 (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))) (sqrt.f64 2)))
1.9s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
1.1s	(-.f64 (.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))

Compiler

Compiled 15785 to 13078 computations (17.1% saved)

simplify1.5s (1.6%)

Algorithm

1×	egg-herbie

Rules

676×	`associate-/l*_binary64_23`
581×	`times-frac_binary64_84`
323×	`associate-/l/_binary64_25`
309×	`associate-/r/_binary64_24`
157×	`*-commutative_binary64_9`
89×	`cancel-sign-sub-inv_binary64_44`
82×	`+-commutative_binary64_8`
70×	`sub-neg_binary64_71`
60×	`associate-/r_binary64_22` `associate-r*_binary64_18`
56×	`distribute-rgt-in_binary64_28`
50×	`distribute-rgt-neg-in_binary64_36`
49×	`unswap-sqr_binary64_46` `distribute-lft-in_binary64_27`
46×	`distribute-neg-in_binary64_39`
45×	`associate-+r+_binary64_10`
44×	`associate-*l/_binary64_21`
43×	`neg-sub0_binary64_73`
38×	`distribute-lft-neg-in_binary64_35`
37×	`neg-mul-1_binary64_74` `distribute-rgt-out_binary64_31`
34×	`sqr-pow_binary64_50`
32×	`associate-*r/_binary64_20`
13×	`associate--l+_binary64_15`
12×	`pow-sqr_binary64_51`
10×	`unpow3_binary64_144` `cube-mult_binary64_108` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `distribute-neg-frac_binary64_42` `associate-l_binary64_19` `associate--r+_binary64_14`
9×	`distribute-lft-out_binary64_29`
7×	`cube-prod_binary64_106` `swap-sqr_binary64_45`
6×	`exp-prod_binary64_130` `rem-sqrt-square_binary64_91` `distribute-lft-neg-out_binary64_37`
5×	`unpow2_binary64_143` `pow-plus_binary64_141` `cube-unmult_binary64_115` `div-sub_binary64_83`
4×	`log-div_binary64_165` `log-prod_binary64_164` `unsub-neg_binary64_72` `remove-double-div_binary64_54` `distribute-rgt-out--_binary64_32`
3×	`exp-sum_binary64_124` `cube-div_binary64_107` `*-rgt-identity_binary64_68` `difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30`
2×	`div-exp_binary64_129` `rem-square-sqrt_binary64_90` `*-inverses_binary64_58`
1×	`rec-exp_binary64_128` `prod-exp_binary64_127` `1-exp_binary64_122` `associate--r-_binary64_17`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `*-lft-identity_binary64_67` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt-neg-out_binary64_38` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate--l-_binary64_16` `associate-+l-_binary64_13` `associate-+r-_binary64_12` `associate-+l+_binary64_11`

Counts

346 → 662

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	690	24045
1	1829	23140

prune3.4s (3.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	650	12	662
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	654	12	666

Error

5.3b

Counts

666 → 12

Compiler

Compiled 38542 to 22924 computations (40.5% saved)

localize30.0ms (0%)

Local error

Found 4 expressions with local error:

3.7b	(/.f64 x (*.f64 l l))
3.8b	(/.f64 (*.f64 x x) l)
4.0b	(+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))
28.5b	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 x (.f64 l l))) (+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (.f64 x x) l)))))))

rewrite332.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

44×	`associate-*r/_binary64_20` `frac-add_binary64_86`
17×	`flip3-+_binary64_81` `flip-+_binary64_52`
14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-div_binary64_95`
11×	`*-un-lft-identity_binary64_78`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84`
5×	`pow1_binary64_139`
4×	`frac-times_binary64_88` `associate-l/_binary64_21` `sqrt-prod_binary64_94` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/l_binary64_23` `associate-/r*_binary64_22`
2×	`distribute-rgt-in_binary64_28` `associate-+l+_binary64_11` `distribute-lft-in_binary64_27` `associate-+r+_binary64_10` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `distribute-lft-out_binary64_29` `rem-sqrt-square_binary64_91` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 95

Calls

4 calls:

30.0ms	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 x (.f64 l l))) (+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (.f64 x x) l)))))))
19.0ms	(+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))
5.0ms	(/.f64 (*.f64 x x) l)
4.0ms	(/.f64 x (*.f64 l l))

Compiler

Compiled 7719 to 1916 computations (75.2% saved)

series3.4s (3.6%)

Error

0.4b

Counts

4 → 57

Calls

4 calls:

2.0s	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 x (.f64 l l))) (+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (.f64 x x) l)))))))
974.0ms	(+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))
123.0ms	(/.f64 x (*.f64 l l))
115.0ms	(/.f64 (*.f64 x x) l)

Compiler

Compiled 9948 to 7875 computations (20.8% saved)

simplify1.3s (1.4%)

Algorithm

1×	egg-herbie

Rules

332×	`distribute-rgt-in_binary64_28`
324×	`distribute-lft-in_binary64_27`
304×	`associate-*l/_binary64_21`
281×	`times-frac_binary64_84`
248×	`associate-/r*_binary64_22`
191×	`associate-/l*_binary64_23`
143×	`*-commutative_binary64_9`
74×	`associate-/r/_binary64_24`
72×	`+-commutative_binary64_8`
64×	`cancel-sign-sub-inv_binary64_44`
60×	`associate-r_binary64_18`
52×	`sub-neg_binary64_71`
50×	`sqr-pow_binary64_50`
45×	`distribute-rgt-neg-in_binary64_36`
41×	`unswap-sqr_binary64_46`
34×	`neg-sub0_binary64_73`
33×	`distribute-neg-in_binary64_39` `distribute-lft-neg-in_binary64_35` `associate-/l/_binary64_25` `associate-l_binary64_19`
32×	`neg-mul-1_binary64_74`
30×	`associate-*r/_binary64_20`
29×	`distribute-rgt-out_binary64_31`
24×	`pow-sqr_binary64_51` `associate-+r+_binary64_10`
22×	`unpow3_binary64_144`
19×	`cube-mult_binary64_108`
14×	`distribute-neg-frac_binary64_42`
12×	`cube-div_binary64_107` `cube-prod_binary64_106`
10×	`distribute-lft-neg-out_binary64_37`
9×	`swap-sqr_binary64_45`
8×	`distribute-rgt-out--_binary64_32`
7×	`log-div_binary64_165` `associate--r+_binary64_14`
6×	`pow-plus_binary64_141` `associate--l+_binary64_15`
4×	`log-prod_binary64_164` `exp-prod_binary64_130` `cube-unmult_binary64_115` `mul-1-neg_binary64_70` `difference-of-squares_binary64_47` `distribute-lft-out_binary64_29` `associate-+r-_binary64_12`
3×	`unpow2_binary64_143` `exp-sum_binary64_124` `*-rgt-identity_binary64_68`
2×	`rem-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90` `unsub-neg_binary64_72` `/-rgt-identity_binary64_69` `count-2_binary64_26`
1×	`exp-lft-sqr_binary64_133` `prod-exp_binary64_127` `1-exp_binary64_122` `*-inverses_binary64_58`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `div-sub_binary64_83` `*-lft-identity_binary64_67` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt-neg-out_binary64_38` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `distribute-lft-out--_binary64_30` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate-+l-_binary64_13` `associate-+l+_binary64_11`

Counts

152 → 437

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	466	10122
1	1439	8827

prune1.8s (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	431	6	437
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	438	11	449

Error

0.1b

Counts

449 → 11

Compiler

Compiled 42517 to 12499 computations (70.6% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

3.3b	(+.f64 (/.f64 t (/.f64 x t)) (*.f64 (/.f64 t x) (/.f64 t x)))
3.8b	(/.f64 (*.f64 x x) l)
4.0b	(+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))
28.5b	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 1 (/.f64 l (/.f64 x l)))) (+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))))

rewrite461.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

47×	`frac-add_binary64_86`
45×	`associate-*r/_binary64_20`
18×	`flip3-+_binary64_81` `flip-+_binary64_52`
14×	`sqrt-div_binary64_95`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117` `add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
5×	`pow1_binary64_139` `frac-times_binary64_88` `associate-*l/_binary64_21`
4×	`sqrt-prod_binary64_94`
3×	`times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`distribute-lft-out_binary64_29` `sum-log_binary64_169` `distribute-rgt-in_binary64_28` `associate-+l+_binary64_11` `distribute-lft-in_binary64_27` `associate-+r+_binary64_10` `+-commutative_binary64_8` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23` `associate-/r/_binary64_24`

Counts

4 → 89

Calls

4 calls:

142.0ms	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 1 (/.f64 l (/.f64 x l)))) (+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))))
25.0ms	(+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))
15.0ms	(+.f64 (/.f64 t (/.f64 x t)) (*.f64 (/.f64 t x) (/.f64 t x)))
5.0ms	(/.f64 (*.f64 x x) l)

Compiler

Compiled 7757 to 2047 computations (73.6% saved)

series3.4s (3.6%)

Error

0.1b

Counts

4 → 60

Calls

4 calls:

1.9s	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 1 (/.f64 l (/.f64 x l)))) (+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))))
992.0ms	(+.f64 (.f64 4 (+.f64 (/.f64 t (/.f64 x t)) (.f64 (/.f64 t x) (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 (*.f64 x x) l)))))
232.0ms	(+.f64 (/.f64 t (/.f64 x t)) (*.f64 (/.f64 t x) (/.f64 t x)))
110.0ms	(/.f64 (*.f64 x x) l)

Compiler

Compiled 10348 to 8272 computations (20.1% saved)

simplify1.5s (1.6%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-l_binary64_19`
348×	`distribute-rgt-in_binary64_28`
336×	`distribute-lft-in_binary64_27`
238×	`associate-*l/_binary64_21`
215×	`times-frac_binary64_84`
210×	`associate-*r/_binary64_20`
199×	`associate-/r*_binary64_22`
163×	`associate-/l*_binary64_23`
145×	`*-commutative_binary64_9`
86×	`associate-/r/_binary64_24`
76×	`+-commutative_binary64_8`
62×	`cancel-sign-sub-inv_binary64_44`
57×	`associate-r_binary64_18`
51×	`sqr-pow_binary64_50`
48×	`sub-neg_binary64_71`
42×	`distribute-rgt-neg-in_binary64_36`
36×	`unswap-sqr_binary64_46`
32×	`neg-sub0_binary64_73` `distribute-neg-in_binary64_39`
30×	`neg-mul-1_binary64_74` `distribute-lft-neg-in_binary64_35`
27×	`distribute-rgt-out_binary64_31`
24×	`associate-/l/_binary64_25` `associate-+r+_binary64_10`
22×	`unpow3_binary64_144` `pow-sqr_binary64_51`
20×	`*-lft-identity_binary64_67`
19×	`cube-mult_binary64_108`
14×	`distribute-neg-frac_binary64_42`
13×	`cube-prod_binary64_106`
11×	`cube-div_binary64_107`
10×	`distribute-lft-neg-out_binary64_37`
9×	`swap-sqr_binary64_45`
8×	`distribute-rgt-out--_binary64_32`
7×	`exp-prod_binary64_130`
6×	`associate--l+_binary64_15` `associate--r+_binary64_14`
5×	`log-div_binary64_165` `pow-plus_binary64_141`
4×	`mul-1-neg_binary64_70` `difference-of-squares_binary64_47` `distribute-lft-out_binary64_29` `associate-+r-_binary64_12`
3×	`unpow2_binary64_143` `exp-sum_binary64_124` `cube-unmult_binary64_115` `/-rgt-identity_binary64_69` `*-rgt-identity_binary64_68`
2×	`log-prod_binary64_164` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90` `unsub-neg_binary64_72`
1×	`exp-lft-sqr_binary64_133` `1-exp_binary64_122` `*-inverses_binary64_58` `count-2_binary64_26`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `div-sub_binary64_83` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt-neg-out_binary64_38` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `distribute-lft-out--_binary64_30` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate-+l-_binary64_13` `associate-+l+_binary64_11`

Counts

149 → 482

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	452	10558
1	1410	9026

prune2.1s (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	481	1	482
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	482	11	493

Error

0.1b

Counts

493 → 11

Compiler

Compiled 46349 to 14378 computations (69% saved)

localize31.0ms (0%)

Local error

Found 4 expressions with local error:

4.0b	(+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x)))))
28.5b	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 1 (/.f64 l (/.f64 x l)))) (.f64 (sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l x) (/.f64 l x)))))) (sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x)))))))))
29.3b	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x))))))
29.3b	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x))))))

rewrite2.3s (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

708×	`associate-*r/_binary64_20`
506×	`sqrt-div_binary64_95`
458×	`frac-add_binary64_86`
291×	`flip3-+_binary64_81` `flip-+_binary64_52`
260×	`frac-times_binary64_88`
70×	`associate-*l/_binary64_21`
10×	`add-sqr-sqrt_binary64_100`
9×	`sqrt-prod_binary64_94`
7×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117`
5×	`distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
4×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `associate-+l+_binary64_11`
3×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`
2×	`associate-+r+_binary64_10`
1×	`sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 260

Calls

4 calls:

130.0ms	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 1 (/.f64 l (/.f64 x l)))) (.f64 (sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l x) (/.f64 l x)))))) (sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x)))))))))
16.0ms	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x))))))
15.0ms	(+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x)))))
14.0ms	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x))))))

Compiler

Compiled 60585 to 11388 computations (81.2% saved)

series5.6s (6%)

Error

0.1b

Counts

4 → 89

Calls

4 calls:

2.0s	(sqrt.f64 (+.f64 (/.f64 2 (/.f64 1 (/.f64 l (/.f64 x l)))) (.f64 (sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l x) (/.f64 l x)))))) (sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x)))))))))
1.1s	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x))))))
1.1s	(sqrt.f64 (+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x))))))
1.0s	(+.f64 (.f64 4 (.f64 (/.f64 t x) (+.f64 t (/.f64 t x)))) (.f64 2 (+.f64 (.f64 t t) (*.f64 (/.f64 l x) (/.f64 l x)))))

Compiler

Compiled 20824 to 15382 computations (26.1% saved)

simplify11.5s (12.2%)

Algorithm

1×	egg-herbie

Rules

582×	`*-commutative_binary64_9`
505×	`associate-r_binary64_18`
462×	`times-frac_binary64_84`
342×	`associate-*l/_binary64_21`
310×	`distribute-rgt-in_binary64_28`
180×	`*-lft-identity_binary64_67`
170×	`+-commutative_binary64_8`
78×	`cancel-sign-sub-inv_binary64_44`
60×	`sub-neg_binary64_71`
50×	`distribute-rgt-neg-in_binary64_36`
49×	`sqr-pow_binary64_50`
45×	`distribute-neg-in_binary64_39`
38×	`unswap-sqr_binary64_46` `associate-+r+_binary64_10`
37×	`neg-sub0_binary64_73`
35×	`distribute-lft-neg-in_binary64_35` `associate-*r/_binary64_20`
34×	`neg-mul-1_binary64_74`
29×	`associate-/r_binary64_22` `associate-l*_binary64_19`
28×	`rem-sqrt-square_binary64_91`
27×	`rem-square-sqrt_binary64_90`
26×	`distribute-rgt-out_binary64_31`
21×	`unpow3_binary64_144` `pow-sqr_binary64_51`
19×	`cube-mult_binary64_108` `distribute-lft-in_binary64_27`
15×	`distribute-neg-frac_binary64_42`
14×	`cube-prod_binary64_106`
13×	`distribute-lft-neg-out_binary64_37`
10×	`difference-of-squares_binary64_47` `associate--l+_binary64_15`
9×	`swap-sqr_binary64_45` `associate-/l*_binary64_23`
8×	`associate--r+_binary64_14`
7×	`cube-div_binary64_107` `distribute-rgt-out--_binary64_32` `distribute-lft-out_binary64_29`
6×	`exp-prod_binary64_130` `mul-1-neg_binary64_70`
5×	`pow-plus_binary64_141`
4×	`associate-+r-_binary64_12`
3×	`unpow2_binary64_143` `unsub-neg_binary64_72` `*-rgt-identity_binary64_68` `associate-/r/_binary64_24`
2×	`exp-sum_binary64_124` `cube-unmult_binary64_115`
1×	`log-prod_binary64_164` `exp-lft-sqr_binary64_133` `prod-exp_binary64_127` `1-exp_binary64_122` `/-rgt-identity_binary64_69` `*-inverses_binary64_58`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `log-div_binary64_165` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `div-sub_binary64_83` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt-neg-out_binary64_38` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `associate-/l/_binary64_25` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate-+l-_binary64_13` `associate-+l+_binary64_11`

Counts

349 → 1954

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1721	75831
1	3426	71028

prune34.0s (36%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	1954	0	1954
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	1954	11	1965

Error

0.1b

Counts

1965 → 11

Compiler

Compiled 413648 to 112909 computations (72.7% saved)

regimes3.8s (4%)

Accuracy

Total 8.2b remaining (96.8%)

Threshold costs 0b (0%)

Compiler

Compiled 37831 to 26370 computations (30.3% saved)

bsearch645.0ms (0.7%)

Steps

Iters	Range		Point
9	4.973685499511632e+141	1.4903751259109817e+148	3.1287133522825756e+147
9	1.0788408303126188e-158	2.3232334138425438e-153	1.094632978090295e-158
9	-1.3828430296055146e-283	-1.520458667321674e-291	-9.937225512484842e-284
10	-9.562079612089908e-147	-8.561739597349485e-164	-8.753971576230512e-164
10	-8.528064677675629e+63	-9.887425445614635e+53	-8.421989759483264e+63

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify52.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

45×	`*-commutative_binary64_9`
43×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
36×	`+-commutative_binary64_8`
25×	`distribute-rgt-neg-in_binary64_36`
24×	`distribute-lft-neg-in_binary64_35`
20×	`sub-neg_binary64_71`
19×	`distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37`
18×	`*-lft-identity_binary64_67`
15×	`cancel-sign-sub-inv_binary64_44`
10×	`unsub-neg_binary64_72`
9×	`*-rgt-identity_binary64_68`
4×	`distribute-neg-frac_binary64_42`
2×	`distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39`
1×	`1-exp_binary64_122` `distribute-frac-neg_binary64_41`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `unpow1_binary64_136` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `cancel-sign-sub_binary64_43`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	102	433
1	152	433
2	181	433
3	210	433
4	274	433
5	302	433
6	325	433
7	338	433
8	343	433
9	344	433

Proof

(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (neg f64 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (- f64 h1 1)) (/ f64 h1 (- f64 h1 1))))) (/ f64 h0 (sqrt f64 2))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 (pow f64 (sqrt f64 2) 2) h1)))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (=> (* f64 1 (/ f64 h0 h1))) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
*-lft-identity_binary64_67 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (=> (neg f64 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (- f64 h1 1)) (/ f64 h1 (- f64 h1 1))))) (/ f64 h0 (sqrt f64 2)))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 (pow f64 (sqrt f64 2) 2) h1)))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
distribute-rgt-neg-in_binary64_36 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (- f64 h1 1)) (/ f64 h1 (=> (- f64 h1 1)))))) (neg f64 (/ f64 h0 (sqrt f64 2))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 (pow f64 (sqrt f64 2) 2) h1)))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
sub-neg_binary64_71 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (=> (- f64 h1 1))) (/ f64 h1 (+ f64 h1 (neg f64 1)))))) (neg f64 (/ f64 h0 (sqrt f64 2))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 (pow f64 (sqrt f64 2) 2) h1)))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
sub-neg_binary64_71 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 (neg f64 1))) (/ f64 h1 (+ f64 h1 (neg f64 1)))))) (neg f64 (/ f64 h0 (sqrt f64 2))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (=> (* f64 (pow f64 (sqrt f64 2) 2) h1))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
*-commutative_binary64_9 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 (neg f64 1))) (/ f64 h1 (+ f64 h1 (=> (neg f64 1))))))) (neg f64 (/ f64 h0 (sqrt f64 2))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
neg-mul-1_binary64_74 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 (=> (neg f64 1)))) (/ f64 h1 (+ f64 h1 (* f64 -1 1)))))) (neg f64 (/ f64 h0 (sqrt f64 2))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
neg-mul-1_binary64_74 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 (* f64 -1 1))) (/ f64 h1 (+ f64 h1 (* f64 -1 1)))))) (=> (neg f64 (/ f64 h0 (sqrt f64 2)))))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
distribute-neg-frac_binary64_42 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 (* f64 -1 1))) (/ f64 h1 (+ f64 h1 (=> (* f64 -1 1))))))) (/ f64 (neg f64 h0) (sqrt f64 2)))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
*-rgt-identity_binary64_68 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 (=> (* f64 -1 1)))) (/ f64 h1 (+ f64 h1 -1))))) (/ f64 (neg f64 h0) (sqrt f64 2)))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))
*-rgt-identity_binary64_68 =>
(if real (<= f64 h0 -8421989759483263970076684814095184187729813550820714517742223360) (/ f64 h0 (* f64 (sqrt f64 (* f64 2 (+ f64 (/ f64 1 (+ f64 h1 -1)) (/ f64 h1 (+ f64 h1 -1))))) (/ f64 (neg f64 h0) (sqrt f64 2)))) (if real (<= f64 h0 -1418935208793367/16209045190941378744189093217543598246142368094697019140608036444104112544581672446873855659949624196438272994575393707743731058888327247296433104820757670652582741419537146576896) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (if real (<= f64 h0 -8318611459514433/83711609936427134449095706957812641450109750914494813081542999091433675869135634569781123344976238916218333821683839595717745725444712034656129512302332615655738810740814304573602145352049774545921517048070675585809233916151552871555980812078727054020087472481926110684847108059786128022165669281792) (/ f64 h0 (/ f64 (- f64 (* f64 (sqrt f64 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1)))) (neg f64 h0)) (* f64 (sqrt f64 (/ f64 1 (+ f64 (/ f64 (/ f64 4 h1) h1) (+ f64 2 (/ f64 4 h1))))) (+ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h0)) (/ f64 (* f64 (/ f64 h2 h1) (/ f64 h2 h1)) h0)))) (sqrt f64 2))) (if real (<= f64 h0 2707360139367727/247330401473104534060502521019647190035131349101211839914063056092897225106531867170316401061243044989597671426016139339351365034306751209967546155101893167916606772148699136) (/ f64 h0 (+ f64 (* f64 2 (/ f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2)))) (+ f64 h0 (/ f64 (pow f64 h2 2) (* f64 h0 (* f64 h1 (pow f64 (sqrt f64 2) 2))))))) (if real (<= f64 h0 3128713352282575632891597201951917857650555333022883311508264089411442103147952949029606472249465347430273717968561570905383429039086463098606845952) (/ f64 h0 (/ f64 (sqrt f64 (+ f64 (/ f64 2 (/ f64 1 (/ f64 h2 (/ f64 h1 h2)))) (* f64 (sqrt f64 (+ f64 (* f64 4 (+ f64 (/ f64 h0 (/ f64 h1 h0)) (* f64 (/ f64 h0 h1) (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (/ f64 h2 (/ f64 (* f64 h1 h1) h2)))))) (sqrt f64 (+ f64 (* f64 4 (* f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 h0 h1)))) (* f64 2 (+ f64 (* f64 h0 h0) (* f64 (/ f64 h2 h1) (/ f64 h2 h1))))))))) (sqrt f64 2))) (/ f64 h0 (+ f64 (/ f64 h0 h1) (+ f64 h0 (/ f64 (/ f64 h2 (/ f64 h0 h2)) (* f64 2 h1))))))))))

end0.0ms (0%)

sample5.6s (5.9%)

Algorithm

1×

intervals

Results

365.0ms	5348×	body	128	valid
315.0ms	1156×	body	1024	valid
222.0ms	857×	body	1024	nan
170.0ms	857×	body	512	valid
107.0ms	1544×	body	128	nan
102.0ms	489×	body	512	nan
74.0ms	572×	body	256	valid
35.0ms	278×	body	256	nan
24.0ms	67×	body	2048	valid

Compiler

Compiled 6239 to 4272 computations (31.5% saved)

Iter	Nodes	Cost
0	102	433
1	152	433
2	181	433
3	210	433
4	274	433
5	302	433
6	325	433
7	338	433
8	343	433
9	344	433

Iter	Nodes	Cost
0	102	433
1	152	433
2	181	433
3	210	433
4	274	433
5	302	433
6	325	433
7	338	433
8	343	433
9	344	433

Details

analyze772.0ms (0.8%)

sample62.0ms (0.1%)

simplify354.0ms (0.4%)

prune17.0ms (0%)

localize17.0ms (0%)

rewrite1.1s (1.1%)

series9.2s (9.8%)

simplify1.5s (1.6%)

prune3.4s (3.6%)

localize30.0ms (0%)

rewrite332.0ms (0.4%)

series3.4s (3.6%)

simplify1.3s (1.4%)

prune1.8s (2%)

localize28.0ms (0%)

rewrite461.0ms (0.5%)

series3.4s (3.6%)

simplify1.5s (1.6%)

prune2.1s (2.2%)

localize31.0ms (0%)

rewrite2.3s (2.5%)

series5.6s (6%)

simplify11.5s (12.2%)

prune34.0s (36%)

regimes3.8s (4%)

bsearch645.0ms (0.7%)

simplify52.0ms (0.1%)

end0.0ms (0%)

sample5.6s (5.9%)

Profiling

Iter	Nodes	Cost
0	102	433
1	152	433
2	181	433
3	210	433
4	274	433
5	302	433
6	325	433
7	338	433
8	343	433
9	344	433