Details

analyze1.1s (4.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

768×	`times-frac_binary64_84`
532×	`div-sub_binary64_83`
475×	`distribute-rgt-in_binary64_28`
322×	`distribute-neg-in_binary64_39`
318×	`cancel-sign-sub-inv_binary64_44`
294×	`distribute-rgt-neg-in_binary64_36`
276×	`associate-/l*_binary64_23`
260×	`distribute-neg-frac_binary64_42`
236×	`associate-l_binary64_19`
222×	`associate-r_binary64_18`
219×	`distribute-lft-in_binary64_27`
208×	`*-commutative_binary64_9`
190×	`associate-/r*_binary64_22`
183×	`distribute-lft-neg-in_binary64_35`
182×	`sub-neg_binary64_71`
132×	`associate-+r+_binary64_10`
128×	`associate-+l+_binary64_11`
107×	`+-commutative_binary64_8`
94×	`neg-mul-1_binary64_74`
92×	`distribute-rgt-out_binary64_31`
82×	`neg-sub0_binary64_73`
75×	`distribute-lft-neg-out_binary64_37`
69×	`associate-*r/_binary64_20`
61×	`associate-*l/_binary64_21`
59×	`associate-/r/_binary64_24`
43×	`-rgt-identity_binary64_68` `-lft-identity_binary64_67`
40×	`distribute-rgt-out--_binary64_32`
34×	`unsub-neg_binary64_72`
32×	`associate--r+_binary64_14`
30×	`associate-+l-_binary64_13`
24×	`distribute-lft-out_binary64_29`
22×	`sub0-neg_binary64_65`
20×	`associate-+r-_binary64_12`
17×	`associate-/l/_binary64_25`
16×	`+-rgt-identity_binary64_63`
15×	`/-rgt-identity_binary64_69`
12×	`distribute-rgt-neg-out_binary64_38` `associate--l+_binary64_15`
10×	`--rgt-identity_binary64_64`
4×	`remove-double-neg_binary64_66` `+-lft-identity_binary64_62` `distribute-rgt1-in_binary64_34`
3×	`mul0-rgt_binary64_61` `mul0-lft_binary64_60`
1×	`1-exp_binary64_122`
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` `pow-plus_binary64_141` `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-prod_binary64_130` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `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-unmult_binary64_115` `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-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `div0_binary64_59` `*-inverses_binary64_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `pow-sqr_binary64_51` `sqr-pow_binary64_50` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `unswap-sqr_binary64_46` `swap-sqr_binary64_45` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft1-in_binary64_33` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `associate--r-_binary64_17` `associate--l-_binary64_16`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	164
1	132	164
2	312	164
3	637	164
4	1194	164
5	2575	164
6	4540	164
7	4990	164
8	5644	164
0	3	3
1	3	3

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)

sample67.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	169×	body	128	valid
10.0ms	35×	body	1024	valid
8.0ms	27×	body	1024	nan
7.0ms	33×	body	512	valid
4.0ms	51×	body	128	nan
3.0ms	18×	body	256	valid
2.0ms	11×	body	512	nan
1.0ms	9×	body	256	nan
0.0ms	1×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify73.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

706×	`div-sub_binary64_83`
508×	`distribute-neg-in_binary64_39`
500×	`distribute-rgt-in_binary64_28`
420×	`distribute-lft-in_binary64_27`
403×	`cancel-sign-sub-inv_binary64_44`
336×	`times-frac_binary64_84`
329×	`sub-neg_binary64_71`
327×	`distribute-neg-frac_binary64_42`
259×	`distribute-rgt-neg-in_binary64_36`
231×	`associate-/l*_binary64_23`
219×	`unsub-neg_binary64_72`
166×	`associate-/r*_binary64_22`
157×	`distribute-lft-neg-in_binary64_35`
136×	`neg-mul-1_binary64_74`
130×	`neg-sub0_binary64_73`
124×	`associate-l_binary64_19`
122×	`associate-r_binary64_18` `associate--r+_binary64_14`
103×	`associate-/r/_binary64_24`
98×	`*-rgt-identity_binary64_68`
96×	`associate-*l/_binary64_21`
90×	`associate--l+_binary64_15`
86×	`*-commutative_binary64_9`
81×	`associate-*r/_binary64_20`
69×	`distribute-rgt-out_binary64_31`
65×	`associate-+l+_binary64_11`
61×	`*-lft-identity_binary64_67`
59×	`associate-+r+_binary64_10`
55×	`distribute-rgt-out--_binary64_32`
47×	`associate--r-_binary64_17`
44×	`remove-double-neg_binary64_66` `distribute-lft-neg-out_binary64_37`
38×	`+-commutative_binary64_8`
35×	`associate-/l/_binary64_25`
30×	`sub0-neg_binary64_65`
24×	`/-rgt-identity_binary64_69` `mul0-rgt_binary64_61` `mul0-lft_binary64_60`
16×	`associate--l-_binary64_16` `associate-+l-_binary64_13`
14×	`--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `div0_binary64_59`
10×	`distribute-lft-out_binary64_29`
9×	`+-lft-identity_binary64_62` `distribute-rgt-neg-out_binary64_38`
7×	`distribute-frac-neg_binary64_41` `associate-+r-_binary64_12`
3×	`remove-double-div_binary64_54` `distribute-rgt1-in_binary64_34` `distribute-lft-out--_binary64_30`
2×	`sqr-neg_binary64_92` `distribute-neg-out_binary64_40`
1×	`1-exp_binary64_122` `distribute-lft1-in_binary64_33`
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` `pow-plus_binary64_141` `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-prod_binary64_130` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `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-unmult_binary64_115` `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` `rem-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `*-inverses_binary64_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `pow-sqr_binary64_51` `sqr-pow_binary64_50` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `unswap-sqr_binary64_46` `swap-sqr_binary64_45` `cancel-sign-sub_binary64_43` `count-2_binary64_26`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	41
1	46	41
2	95	41
3	184	41
4	355	41
5	714	41
6	1619	41
7	3620	41
8	4716	41
9	5192	41

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

44.8b

Counts

1 → 1

Compiler

Compiled 27 to 20 computations (25.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.5b	(*.f64 (sqrt.f64 2) t)
17.1b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.9b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite257.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

44.7b

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117` `associate-l_binary64_19` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `associate-r_binary64_18`
2×	`associate--l+_binary64_15` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r/_binary64_24`
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` `pow-prod-down_binary64_149` `-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`

Counts

4 → 80

Calls

4 calls:

22.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
16.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series5.1s (22%)

Error

5.3b

Counts

4 → 58

Calls

4 calls:

2.6s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
1.3s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
1.0s	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
49.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 9592 to 7988 computations (16.7% saved)

simplify163.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

329×	`cancel-sign-sub-inv_binary64_44`
290×	`times-frac_binary64_84`
260×	`associate-/l*_binary64_23`
243×	`associate-l_binary64_19`
242×	`associate-r_binary64_18`
215×	`associate-/r*_binary64_22`
205×	`*-commutative_binary64_9`
148×	`sub-neg_binary64_71`
144×	`associate-*r/_binary64_20`
136×	`associate-*l/_binary64_21`
132×	`+-commutative_binary64_8`
127×	`unswap-sqr_binary64_46`
101×	`associate-+r+_binary64_10`
84×	`associate-+l+_binary64_11`
77×	`neg-sub0_binary64_73`
70×	`neg-mul-1_binary64_74`
58×	`sqr-pow_binary64_50`
51×	`div-sub_binary64_83`
45×	`*-rgt-identity_binary64_68` `associate-/l/_binary64_25` `associate--l+_binary64_15`
42×	`unsub-neg_binary64_72`
41×	`distribute-rgt-in_binary64_28`
37×	`associate--r+_binary64_14`
36×	`exp-prod_binary64_130` `/-rgt-identity_binary64_69` `distribute-rgt-neg-in_binary64_36` `distribute-lft-in_binary64_27`
33×	`associate-/r/_binary64_24`
31×	`distribute-lft-neg-in_binary64_35`
28×	`distribute-neg-in_binary64_39`
21×	`distribute-rgt-out_binary64_31`
19×	`log-div_binary64_165`
18×	`cube-div_binary64_107`
17×	`cube-prod_binary64_106` `*-lft-identity_binary64_67`
14×	`unpow3_binary64_144`
13×	`cube-mult_binary64_108`
10×	`log-prod_binary64_164`
9×	`exp-sum_binary64_124`
7×	`mul-1-neg_binary64_70` `distribute-lft-out_binary64_29`
6×	`swap-sqr_binary64_45`
5×	`cube-unmult_binary64_115` `pow-sqr_binary64_51` `difference-of-squares_binary64_47` `distribute-neg-frac_binary64_42`
4×	`log-rec_binary64_166` `+-rgt-identity_binary64_63` `associate-+r-_binary64_12`
3×	`unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `exp-diff_binary64_126` `rem-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90`
2×	`pow-plus_binary64_141` `distribute-lft-neg-out_binary64_37` `distribute-rgt-out--_binary64_32` `distribute-lft-out--_binary64_30`
1×	`log-pow_binary64_167` `exp-lft-sqr_binary64_133` `div-exp_binary64_129` `1-exp_binary64_122` `exp-1-e_binary64_121` `*-inverses_binary64_58` `difference-of-sqr--1_binary64_49`
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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-neg_binary64_125` `e-exp-1_binary64_123` `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` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-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_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--r-_binary64_17` `associate--l-_binary64_16` `associate-+l-_binary64_13`

Counts

138 → 101

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	346	6595
1	970	6025
2	4139	6025
3	5155	6025

prune249.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Error

5.3b

Counts

102 → 9

Compiler

Compiled 4456 to 2765 computations (37.9% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

11.4b	(/.f64 (*.f64 t t) x)
18.1b	(/.f64 (.f64 l l) (.f64 x x))
22.0b	(/.f64 (.f64 t t) (.f64 x x))
28.9b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))

rewrite243.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

Rules

33×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`associate-*r/_binary64_20`
16×	`frac-add_binary64_86`
10×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
9×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `flip3-+_binary64_81` `flip-+_binary64_52` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`

Counts

4 → 86

Calls

4 calls:

18.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))
7.0ms	(/.f64 (.f64 l l) (.f64 x x))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5815 to 1665 computations (71.4% saved)

series2.0s (8.5%)

Error

0.3b

Counts

4 → 40

Calls

4 calls:

1.5s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))
142.0ms	(/.f64 (.f64 l l) (.f64 x x))
119.0ms	(/.f64 (.f64 t t) (.f64 x x))
115.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 7538 to 5743 computations (23.8% saved)

simplify146.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

430×	`times-frac_binary64_84`
418×	`associate-l_binary64_19`
237×	`associate-/l*_binary64_23`
230×	`associate-/r*_binary64_22`
215×	`distribute-rgt-in_binary64_28`
205×	`distribute-lft-in_binary64_27`
177×	`associate-l/_binary64_21` `associate-r/_binary64_20`
130×	`*-commutative_binary64_9`
92×	`neg-mul-1_binary64_74`
62×	`+-commutative_binary64_8`
56×	`sub-neg_binary64_71` `associate-r_binary64_18`
55×	`cancel-sign-sub-inv_binary64_44`
46×	`associate-/l/_binary64_25`
42×	`sqr-pow_binary64_50`
39×	`distribute-rgt-neg-in_binary64_36`
35×	`unswap-sqr_binary64_46`
33×	`cube-div_binary64_107` `neg-sub0_binary64_73`
32×	`distribute-neg-in_binary64_39` `associate-/r/_binary64_24`
30×	`log-div_binary64_165`
29×	`distribute-lft-neg-in_binary64_35`
28×	`unpow3_binary64_144`
26×	`cube-prod_binary64_106` `distribute-rgt-out_binary64_31`
23×	`cube-mult_binary64_108`
21×	`log-prod_binary64_164`
20×	`associate-+r+_binary64_10`
19×	`distribute-neg-frac_binary64_42`
10×	`swap-sqr_binary64_45`
9×	`div-sub_binary64_83`
8×	`distribute-lft-neg-out_binary64_37`
6×	`pow-plus_binary64_141` `difference-of-squares_binary64_47` `distribute-rgt-out--_binary64_32` `distribute-lft-out_binary64_29` `associate--l+_binary64_15` `associate--r+_binary64_14`
5×	`exp-prod_binary64_130` `cube-unmult_binary64_115` `rem-sqrt-square_binary64_91`
4×	`mul-1-neg_binary64_70` `associate-+r-_binary64_12`
3×	`log-pow_binary64_167` `unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `pow-sqr_binary64_51` `distribute-lft-out--_binary64_30` `count-2_binary64_26`
2×	`rem-square-sqrt_binary64_90` `unsub-neg_binary64_72` `/-rgt-identity_binary64_69`
1×	`log-rec_binary64_166` `1-exp_binary64_122` `*-rgt-identity_binary64_68`
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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `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_58` `+-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` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate-+l-_binary64_13` `associate-+l+_binary64_11`

Counts

126 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	5725
1	1245	5165
2	4817	5145
3	4975	5145

prune234.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	91	10	101

Error

0.3b

Counts

101 → 10

Compiler

Compiled 5708 to 2375 computations (58.4% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

22.0b	(/.f64 (.f64 t t) (.f64 x x))
22.0b	(/.f64 (.f64 t t) (.f64 x x))
29.8b	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
29.8b	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))

rewrite410.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

48×	`associate-*r/_binary64_20`
44×	`frac-add_binary64_86`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `cbrt-div_binary64_110`
22×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111`
6×	`add-cube-cbrt_binary64_113` `cbrt-prod_binary64_109` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`pow1_binary64_139` `add-log-exp_binary64_117`
2×	`pow1/3_binary64_160` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 92

Calls

4 calls:

20.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
17.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 11820 to 2320 computations (80.4% saved)

series4.2s (18.2%)

Error

0.3b

Counts

4 → 46

Calls

4 calls:

1.9s	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
1.9s	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
154.0ms	(/.f64 (.f64 t t) (.f64 x x))
145.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 14632 to 9752 computations (33.4% saved)

simplify280.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-r_binary64_18`
338×	`associate-l_binary64_19`
274×	`distribute-rgt-in_binary64_28`
267×	`distribute-lft-in_binary64_27`
204×	`times-frac_binary64_84`
160×	`associate-*r/_binary64_20`
144×	`associate-*l/_binary64_21`
138×	`associate-/l*_binary64_23`
131×	`associate-/r*_binary64_22`
111×	`*-commutative_binary64_9`
51×	`sqr-pow_binary64_50`
50×	`cancel-sign-sub-inv_binary64_44`
49×	`+-commutative_binary64_8`
47×	`associate-+l+_binary64_11`
45×	`associate-+r+_binary64_10`
40×	`sub-neg_binary64_71`
36×	`distribute-rgt-neg-in_binary64_36`
29×	`unpow3_binary64_144`
28×	`distribute-lft-neg-in_binary64_35`
26×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73` `unswap-sqr_binary64_46`
21×	`cube-div_binary64_107`
18×	`distribute-neg-frac_binary64_42`
17×	`exp-sum_binary64_124`
16×	`log-div_binary64_165` `log-prod_binary64_164` `cube-prod_binary64_106`
15×	`cube-mult_binary64_108` `distribute-rgt-out_binary64_31` `associate-/r/_binary64_24`
14×	`associate--r+_binary64_14`
13×	`div-sub_binary64_83`
12×	`unpow1/3_binary64_145` `exp-prod_binary64_130`
10×	`distribute-neg-in_binary64_39` `distribute-lft-neg-out_binary64_37`
9×	`associate--l+_binary64_15`
7×	`swap-sqr_binary64_45` `distribute-lft-out_binary64_29`
6×	`log-pow_binary64_167` `exp-diff_binary64_126` `difference-of-squares_binary64_47`
5×	`unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `distribute-rgt-out--_binary64_32`
4×	`cube-unmult_binary64_115` `distribute-rgt-neg-out_binary64_38` `associate-+l-_binary64_13` `associate-+r-_binary64_12`
3×	`pow-plus_binary64_141` `associate-/l/_binary64_25`
2×	`log-rec_binary64_166` `pow-sqr_binary64_51` `cancel-sign-sub_binary64_43` `distribute-lft-out--_binary64_30` `count-2_binary64_26`
1×	`1-exp_binary64_122` `rem-3cbrt-lft_binary64_103` `rem-sqrt-square_binary64_91` `*-rgt-identity_binary64_68` `distribute-rgt1-in_binary64_34`
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` `pow-base-0_binary64_162` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `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-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `rem-square-sqrt_binary64_90` `unsub-neg_binary64_72` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `-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_58` `+-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` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft1-in_binary64_33` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

138 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	332	10640
1	1104	9708
2	4847	9552
3	4994	9552
4	4982	9552

prune417.0ms (1.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	102	10	112

Error

0.3b

Counts

112 → 10

Compiler

Compiled 11072 to 3574 computations (67.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 4 (*.f64 x x)) (+.f64 2 (/.f64 4 x)))
0.5b	(.f64 t (sqrt.f64 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 2 (/.f64 4 x)))))
0.5b	(*.f64 (sqrt.f64 2) t)
0.7b	(/.f64 4 (*.f64 x x))

rewrite200.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

22×	`*-un-lft-identity_binary64_78`
20×	`add-sqr-sqrt_binary64_100`
13×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
12×	`add-cube-cbrt_binary64_113`
11×	`associate-r_binary64_18`
10×	`sqrt-prod_binary64_94`
9×	`add-log-exp_binary64_117` `associate-l_binary64_19`
8×	`pow1_binary64_139`
6×	`distribute-lft-out_binary64_29`
4×	`unswap-sqr_binary64_46` `flip3-+_binary64_81` `frac-add_binary64_86` `sqrt-div_binary64_95` `associate-*r/_binary64_20` `flip-+_binary64_52`
3×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `times-frac_binary64_84` `associate-/l*_binary64_23` `sum-log_binary64_169`
2×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `pow-prod-down_binary64_149` `*-commutative_binary64_9`
1×	`frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/r*_binary64_22` `associate-+r+_binary64_10` `+-commutative_binary64_8`

Counts

4 → 88

Calls

4 calls:

19.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 2 (/.f64 4 x)))))
15.0ms	(+.f64 (/.f64 4 (*.f64 x x)) (+.f64 2 (/.f64 4 x)))
5.0ms	(*.f64 (sqrt.f64 2) t)
5.0ms	(/.f64 4 (*.f64 x x))

Compiler

Compiled 2610 to 1869 computations (28.4% saved)

series401.0ms (1.7%)

Error

0.3b

Counts

4 → 20

Calls

4 calls:

236.0ms	(.f64 t (sqrt.f64 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 2 (/.f64 4 x)))))
51.0ms	(*.f64 (sqrt.f64 2) t)
50.0ms	(+.f64 (/.f64 4 (*.f64 x x)) (+.f64 2 (/.f64 4 x)))
41.0ms	(/.f64 4 (*.f64 x x))

Compiler

Compiled 1010 to 894 computations (11.5% saved)

simplify118.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64_44`
468×	`distribute-rgt-in_binary64_28`
432×	`distribute-lft-in_binary64_27`
293×	`*-commutative_binary64_9`
175×	`associate-*l/_binary64_21`
162×	`times-frac_binary64_84`
160×	`associate-*r/_binary64_20`
159×	`associate-l_binary64_19`
143×	`associate-/l*_binary64_23`
141×	`associate-r_binary64_18`
127×	`sub-neg_binary64_71`
122×	`distribute-neg-frac_binary64_42`
99×	`associate-+l+_binary64_11`
94×	`neg-mul-1_binary64_74`
86×	`associate-+r+_binary64_10`
83×	`unswap-sqr_binary64_46`
82×	`div-sub_binary64_83`
81×	`associate-/r*_binary64_22`
76×	`sqr-pow_binary64_50`
74×	`distribute-rgt-neg-in_binary64_36`
68×	`unsub-neg_binary64_72` `distribute-lft-neg-in_binary64_35`
63×	`+-commutative_binary64_8`
50×	`neg-sub0_binary64_73`
47×	`*-lft-identity_binary64_67`
46×	`*-rgt-identity_binary64_68`
43×	`log-prod_binary64_164`
42×	`associate-/l/_binary64_25`
38×	`exp-prod_binary64_130`
37×	`cube-prod_binary64_106`
33×	`cube-div_binary64_107`
32×	`log-div_binary64_165`
27×	`associate--l+_binary64_15`
25×	`swap-sqr_binary64_45` `distribute-rgt-out_binary64_31`
20×	`associate-/r/_binary64_24`
19×	`associate--r+_binary64_14`
17×	`associate-+l-_binary64_13`
16×	`unpow3_binary64_144` `distribute-lft-neg-out_binary64_37` `distribute-rgt-out--_binary64_32` `associate-+r-_binary64_12`
15×	`pow-sqr_binary64_51` `distribute-neg-in_binary64_39` `distribute-lft-out_binary64_29`
14×	`+-rgt-identity_binary64_63`
13×	`exp-sum_binary64_124`
12×	`distribute-rgt-neg-out_binary64_38`
11×	`cube-mult_binary64_108`
8×	`pow-plus_binary64_141` `sub0-neg_binary64_65` `distribute-lft-out--_binary64_30`
7×	`prod-exp_binary64_127` `cube-unmult_binary64_115` `rem-sqrt-square_binary64_91`
6×	`distribute-rgt1-in_binary64_34`
5×	`unpow2_binary64_143` `unpow1/2_binary64_142`
4×	`log-rec_binary64_166` `difference-of-squares_binary64_47`
3×	`log-pow_binary64_167` `unpow1_binary64_136` `/-rgt-identity_binary64_69`
2×	`exp-diff_binary64_126` `rem-square-sqrt_binary64_90` `count-2_binary64_26`
1×	`1-exp_binary64_122` `exp-1-e_binary64_121` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `*-inverses_binary64_58` `distribute-lft1-in_binary64_33`
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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-neg_binary64_125` `e-exp-1_binary64_123` `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` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `--rgt-identity_binary64_64` `+-lft-identity_binary64_62` `+-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` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

108 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	1825
1	436	1717
2	1329	1672
3	3882	1672
4	4783	1672
5	4923	1672

prune90.0ms (0.4%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	58	11	69

Error

0.3b

Counts

69 → 11

Compiler

Compiled 1503 to 1100 computations (26.8% saved)

regimes2.5s (10.8%)

Accuracy

Total 11.6b remaining (96.9%)

Threshold costs 0b (0%)

Compiler

Compiled 25830 to 17011 computations (34.1% saved)

bsearch493.0ms (2.1%)

Steps

Iters	Range		Point
8	5.0105556770902745e+30	2.098564712608581e+34	1.2822754990186077e+34
8	5.3905340768114946e-189	6.9280865136994265e-186	5.463357865450902e-189
9	-5.549523958144308e-231	-3.6692232838675215e-236	-3.702260431372761e-236
10	-1.4517572256425403e-27	-8.955976814391053e-38	-1.43838900620848e-27

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64_9`
12×	`+-commutative_binary64_8`
11×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
5×	`sub-neg_binary64_71` `*-rgt-identity_binary64_68` `distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35`
4×	`distribute-rgt-neg-out_binary64_38`
3×	`*-lft-identity_binary64_67` `distribute-lft-neg-out_binary64_37`
1×	`1-exp_binary64_122` `unsub-neg_binary64_72` `cancel-sign-sub-inv_binary64_44`
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` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	201
1	80	201
2	91	201
3	98	201
4	115	201
5	114	201
6	112	201

end0.0ms (0%)

sample4.4s (18.8%)

Algorithm

1×

intervals

Results

420.0ms	5345×	body	128	valid
350.0ms	1174×	body	1024	valid
233.0ms	835×	body	1024	nan
186.0ms	872×	body	512	valid
110.0ms	1527×	body	128	nan
104.0ms	504×	body	512	nan
77.0ms	532×	body	256	valid
39.0ms	260×	body	256	nan
28.0ms	77×	body	2048	valid

Compiler

Compiled 3709 to 2467 computations (33.5% saved)

Details

analyze1.1s (4.6%)

sample67.0ms (0.3%)

simplify73.0ms (0.3%)

prune2.0ms (0%)

localize22.0ms (0.1%)

rewrite257.0ms (1.1%)

series5.1s (22%)

simplify163.0ms (0.7%)

prune249.0ms (1.1%)

localize30.0ms (0.1%)

rewrite243.0ms (1%)

series2.0s (8.5%)

simplify146.0ms (0.6%)

prune234.0ms (1%)

localize33.0ms (0.1%)

rewrite410.0ms (1.8%)

series4.2s (18.2%)

simplify280.0ms (1.2%)

prune417.0ms (1.8%)

localize16.0ms (0.1%)

rewrite200.0ms (0.9%)

series401.0ms (1.7%)

simplify118.0ms (0.5%)

prune90.0ms (0.4%)

regimes2.5s (10.8%)

bsearch493.0ms (2.1%)

simplify10.0ms (0%)

end0.0ms (0%)

sample4.4s (18.8%)

Profiling