Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample12.0ms (0.3%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify148.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64_9`
1×	`associate-l_binary64_19` `associate-r_binary64_18`
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` `1-exp_binary64_122` `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` `times-frac_binary64_84` `div-sub_binary64_83` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `sub-neg_binary64_71` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `-rgt-identity_binary64_68` `-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` `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-inv_binary64_44` `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` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37` `distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `distribute-rgt-out--_binary64_32` `distribute-rgt-out_binary64_31` `distribute-lft-out--_binary64_30` `distribute-lft-out_binary64_29` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `count-2_binary64_26` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `associate-/l_binary64_23` `associate-/r_binary64_22` `associate-l/_binary64_21` `associate-*r/_binary64_20` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--l+_binary64_15` `associate--r+_binary64_14` `associate-+l-_binary64_13` `associate-+r-_binary64_12` `associate-+l+_binary64_11` `associate-+r+_binary64_10` `+-commutative_binary64_8`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	11	9

prune1.0ms (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

30.1b

Counts

1 → 1

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(.f64 2 (.f64 x x))
28.9b	(sqrt.f64 (.f64 2 (.f64 x x)))

rewrite50.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

30.0b

Rules

13×	`pow1_binary64_139`
7×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
6×	`pow-prod-down_binary64_149`
4×	`add-sqr-sqrt_binary64_100`
3×	`add-cube-cbrt_binary64_113` `sqrt-pow1_binary64_96` `-un-lft-identity_binary64_78` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-l*_binary64_19`
2×	`add-log-exp_binary64_117`
1×	`pow1/2_binary64_158` `sqrt-prod_binary64_94` `unswap-sqr_binary64_46` `associate-r_binary64_18` `*-commutative_binary64_9`

Counts

2 → 31

Calls

2 calls:

6.0ms	(.f64 2 (.f64 x x))
6.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 344 to 213 computations (38.1% saved)

series87.0ms (2.1%)

Error

0.2b

Counts

2 → 6

Calls

2 calls:

45.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
36.0ms	(.f64 2 (.f64 x x))

Compiler

Compiled 96 to 91 computations (5.2% saved)

simplify173.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

430×	`associate-/l*_binary64_23`
310×	`distribute-rgt-out_binary64_31`
270×	`associate-*l/_binary64_21`
264×	`associate-l_binary64_19`
222×	`*-commutative_binary64_9`
218×	`associate-+l+_binary64_11`
217×	`associate-*r/_binary64_20`
191×	`unswap-sqr_binary64_46`
157×	`associate-/r/_binary64_24` `associate-r_binary64_18`
151×	`associate-+r+_binary64_10`
150×	`sqr-pow_binary64_50`
146×	`log-div_binary64_165`
140×	`cube-div_binary64_107`
109×	`exp-prod_binary64_130`
105×	`log-prod_binary64_164`
104×	`associate-/r*_binary64_22`
91×	`cube-prod_binary64_106`
88×	`associate-/l/_binary64_25`
83×	`pow-sqr_binary64_51`
78×	`swap-sqr_binary64_45`
77×	`distribute-rgt-in_binary64_28`
52×	`distribute-lft-in_binary64_27` `associate-+l-_binary64_13`
48×	`*-lft-identity_binary64_67`
47×	`distribute-lft-out_binary64_29`
38×	`exp-sqrt_binary64_131`
36×	`pow-plus_binary64_141`
34×	`associate-+r-_binary64_12`
29×	`cancel-sign-sub-inv_binary64_44`
27×	`/-rgt-identity_binary64_69` `associate--l+_binary64_15`
21×	`associate--l-_binary64_16`
20×	`distribute-rgt1-in_binary64_34`
19×	`sub-neg_binary64_71`
18×	`exp-lft-sqr_binary64_133` `times-frac_binary64_84`
17×	`count-2_binary64_26`
16×	`*-rgt-identity_binary64_68` `distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35` `associate--r+_binary64_14`
14×	`log-pow_binary64_167`
12×	`unpow3_binary64_144` `exp-sum_binary64_124` `distribute-neg-frac_binary64_42`
10×	`cube-mult_binary64_108`
9×	`+-commutative_binary64_8`
8×	`cube-unmult_binary64_115` `distribute-lft1-in_binary64_33`
7×	`unsub-neg_binary64_72`
6×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
5×	`rem-sqrt-square_binary64_91` `distribute-neg-out_binary64_40`
4×	`log-rec_binary64_166` `associate--r-_binary64_17`
3×	`unpow1_binary64_136` `prod-exp_binary64_127` `+-lft-identity_binary64_62`
2×	`exp-diff_binary64_126` `div-sub_binary64_83` `mul-1-neg_binary64_70` `mul0-rgt_binary64_61` `mul0-lft_binary64_60`
1×	`unpow2_binary64_143` `pow-base-1_binary64_138` `div-exp_binary64_129` `rec-exp_binary64_128` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `rem-square-sqrt_binary64_90` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `*-inverses_binary64_58` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `distribute-neg-in_binary64_39` `distribute-rgt-out--_binary64_32` `distribute-lft-out--_binary64_30`
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` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `unpow0_binary64_137` `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-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` `+-rgt-identity_binary64_63` `div0_binary64_59` `+-inverses_binary64_57` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37`

Counts

37 → 85

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	369
1	93	318
2	284	318
3	583	318
4	1176	318
5	3043	318

prune77.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	4	86

Error

0.2b

Counts

86 → 4

Compiler

Compiled 1086 to 570 computations (47.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) (fabs.f64 x))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-sqr-sqrt_binary64_100`
6×	`associate-l_binary64_19`
4×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `sqrt-prod_binary64_94`
3×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `associate-r_binary64_18`
2×	`unswap-sqr_binary64_46`
1×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

1 → 22

Calls

1 calls:

5.0ms

(*.f64 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 240 to 167 computations (30.4% saved)

series51.0ms (1.3%)

Error

0.2b

Counts

1 → 3

Calls

1 calls:

49.0ms

(*.f64 (sqrt.f64 2) (fabs.f64 x))

Compiler

Compiled 45 to 41 computations (8.9% saved)

simplify371.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

470×	`distribute-lft-out--_binary64_30`
329×	`associate-/l/_binary64_25`
317×	`log-prod_binary64_164`
291×	`log-div_binary64_165`
253×	`associate-/r*_binary64_22`
248×	`distribute-rgt-out_binary64_31`
220×	`distribute-rgt-out--_binary64_32`
208×	`*-commutative_binary64_9`
207×	`associate-l_binary64_19`
206×	`times-frac_binary64_84`
201×	`unswap-sqr_binary64_46`
169×	`associate-/r/_binary64_24`
137×	`cube-div_binary64_107`
133×	`cancel-sign-sub-inv_binary64_44`
119×	`exp-prod_binary64_130`
112×	`cube-prod_binary64_106`
108×	`sqr-pow_binary64_50` `associate-r_binary64_18`
81×	`swap-sqr_binary64_45`
73×	`log-pow_binary64_167`
69×	`pow-sqr_binary64_51`
67×	`distribute-rgt-in_binary64_28`
59×	`associate-/l*_binary64_23`
53×	`distribute-rgt-neg-in_binary64_36`
52×	`pow-plus_binary64_141` `distribute-lft-in_binary64_27`
41×	`distribute-lft-neg-in_binary64_35`
38×	`associate-*l/_binary64_21`
32×	`unpow3_binary64_144`
31×	`log-rec_binary64_166`
28×	`exp-to-pow_binary64_140` `*-lft-identity_binary64_67`
27×	`*-rgt-identity_binary64_68`
23×	`distribute-neg-frac_binary64_42` `distribute-rgt1-in_binary64_34`
20×	`associate--l+_binary64_15`
16×	`exp-sqrt_binary64_131` `/-rgt-identity_binary64_69`
15×	`associate-*r/_binary64_20` `associate--r+_binary64_14` `associate-+l+_binary64_11`
14×	`sub-neg_binary64_71`
13×	`exp-lft-sqr_binary64_133`
11×	`associate-+r+_binary64_10`
8×	`cube-unmult_binary64_115` `cube-mult_binary64_108` `neg-mul-1_binary64_74` `remove-double-div_binary64_54` `distribute-neg-in_binary64_39` `distribute-lft1-in_binary64_33` `associate--r-_binary64_17` `associate--l-_binary64_16`
7×	`+-commutative_binary64_8`
6×	`exp-sum_binary64_124` `associate-+r-_binary64_12`
5×	`prod-exp_binary64_127` `associate-+l-_binary64_13`
4×	`pow-base-1_binary64_138` `neg-sub0_binary64_73` `+-inverses_binary64_57`
3×	`div-sub_binary64_83` `difference-of-squares_binary64_47` `distribute-lft-out_binary64_29` `count-2_binary64_26`
2×	`exp-diff_binary64_126` `rem-log-exp_binary64_119` `rem-sqrt-square_binary64_91`
1×	`log-E_binary64_168` `div-exp_binary64_129` `rec-exp_binary64_128` `1-exp_binary64_122` `exp-1-e_binary64_121` `sqr-abs_binary64_93` `rem-square-sqrt_binary64_90` `sub0-neg_binary64_65` `div0_binary64_59` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-neg-out_binary64_40`
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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow2_binary64_143` `unpow1/2_binary64_142` `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-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-neg_binary64_92` `unsub-neg_binary64_72` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `lft-mult-inverse_binary64_56` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37`

Counts

25 → 12

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	282
1	67	270
2	178	270
3	310	270
4	489	270
5	790	270
6	1726	270
7	4557	270

prune18.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	8	4	12
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	10	6	16

Error

0.0b

Counts

16 → 6

Compiler

Compiled 176 to 134 computations (23.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

rewrite92.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`pow1_binary64_139` `add-exp-log_binary64_116`
12×	`add-sqr-sqrt_binary64_100`
10×	`associate-r_binary64_18`
9×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `add-cbrt-cube_binary64_114` `cbrt-unprod_binary64_111`
8×	`cbrt-prod_binary64_109`
6×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`associate-l_binary64_19` `sqrt-prod_binary64_94`
3×	`unswap-sqr_binary64_46`
2×	`add-log-exp_binary64_117` `*-commutative_binary64_9`

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
6.0ms	(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))

Compiler

Compiled 1021 to 860 computations (15.8% saved)

series184.0ms (4.6%)

Error

0.0b

Counts

2 → 6

Calls

2 calls:

132.0ms	(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
48.0ms	(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 180 to 170 computations (5.6% saved)

simplify356.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

529×	`distribute-rgt-in_binary64_28`
511×	`associate-/r*_binary64_22`
488×	`distribute-lft-in_binary64_27`
444×	`unswap-sqr_binary64_46`
251×	`associate-/l*_binary64_23`
206×	`*-commutative_binary64_9`
176×	`sqr-pow_binary64_50`
148×	`associate-/l/_binary64_25`
121×	`associate-l_binary64_19`
105×	`associate-r_binary64_18`
95×	`pow-sqr_binary64_51`
88×	`log-prod_binary64_164`
87×	`distribute-rgt-out_binary64_31`
86×	`exp-prod_binary64_130`
85×	`associate-*r/_binary64_20`
80×	`distribute-lft-out_binary64_29`
73×	`associate-+l+_binary64_11`
61×	`cube-prod_binary64_106`
60×	`associate-*l/_binary64_21`
54×	`times-frac_binary64_84`
53×	`associate-+r+_binary64_10`
43×	`swap-sqr_binary64_45`
31×	`rem-sqrt-square_binary64_91`
30×	`*-rgt-identity_binary64_68`
29×	`pow-plus_binary64_141`
27×	`*-lft-identity_binary64_67`
18×	`log-pow_binary64_167`
17×	`/-rgt-identity_binary64_69` `distribute-rgt1-in_binary64_34`
14×	`cube-unmult_binary64_115`
9×	`log-div_binary64_165` `unpow3_binary64_144` `count-2_binary64_26` `+-commutative_binary64_8`
8×	`cube-div_binary64_107`
7×	`distribute-lft1-in_binary64_33` `associate-/r/_binary64_24`
5×	`cube-mult_binary64_108`
4×	`*-inverses_binary64_58`
3×	`+-rgt-identity_binary64_63` `+-lft-identity_binary64_62`
2×	`rem-cbrt-cube_binary64_102` `rgt-mult-inverse_binary64_55`
1×	`log-rec_binary64_166` `unpow1/3_binary64_145` `pow-base-1_binary64_138` `prod-exp_binary64_127` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `sqr-abs_binary64_93` `rem-square-sqrt_binary64_90` `lft-mult-inverse_binary64_56`
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` `unpow2_binary64_143` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `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` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `e-exp-1_binary64_123` `exp-0_binary64_120` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-cube-cbrt_binary64_101` `sqr-neg_binary64_92` `div-sub_binary64_83` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `sub-neg_binary64_71` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `cancel-sign-sub-inv_binary64_44` `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` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37` `distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35` `distribute-rgt-out--_binary64_32` `distribute-lft-out--_binary64_30` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--l+_binary64_15` `associate--r+_binary64_14` `associate-+l-_binary64_13` `associate-+r-_binary64_12`

Counts

54 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	1158
1	157	640
2	496	622
3	992	622
4	3290	612

prune102.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	67	6	73

Error

0.0b

Counts

73 → 6

Compiler

Compiled 1359 to 1144 computations (15.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))

rewrite82.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`sqrt-prod_binary64_94`
15×	`add-sqr-sqrt_binary64_100`
12×	`associate-l_binary64_19`
10×	`associate-r_binary64_18`
9×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
3×	`unswap-sqr_binary64_46`
2×	`add-log-exp_binary64_117` `*-commutative_binary64_9`

Counts

2 → 50

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))
7.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 858 to 704 computations (17.9% saved)

series112.0ms (2.8%)

Error

0.0b

Counts

2 → 6

Calls

2 calls:

62.0ms	(*.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2)))
46.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 (fabs.f64 x) (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 135 to 125 computations (7.4% saved)

simplify203.0ms (5%)

Algorithm

1×	egg-herbie

Rules

347×	`associate-/r/_binary64_24`
316×	`log-prod_binary64_164`
314×	`unswap-sqr_binary64_46`
311×	`associate-l_binary64_19`
296×	`cube-prod_binary64_106`
230×	`distribute-rgt-out_binary64_31`
216×	`sqr-pow_binary64_50`
213×	`exp-prod_binary64_130`
207×	`times-frac_binary64_84`
200×	`associate-r_binary64_18`
165×	`swap-sqr_binary64_45`
145×	`*-commutative_binary64_9`
135×	`pow-sqr_binary64_51`
134×	`distribute-lft-out_binary64_29`
111×	`log-div_binary64_165`
107×	`cube-div_binary64_107`
95×	`associate-/r*_binary64_22`
93×	`*-rgt-identity_binary64_68`
91×	`*-lft-identity_binary64_67` `distribute-lft-out--_binary64_30`
74×	`associate-/l*_binary64_23`
73×	`distribute-rgt-out--_binary64_32`
32×	`distribute-rgt-in_binary64_28`
31×	`unpow3_binary64_144`
28×	`cube-mult_binary64_108`
27×	`pow-plus_binary64_141`
26×	`log-pow_binary64_167`
23×	`distribute-rgt1-in_binary64_34` `associate-/l/_binary64_25`
22×	`associate-*l/_binary64_21`
20×	`cancel-sign-sub-inv_binary64_44`
17×	`exp-lft-sqr_binary64_133`
15×	`exp-to-pow_binary64_140` `rem-sqrt-square_binary64_91` `sub-neg_binary64_71`
14×	`distribute-rgt-neg-in_binary64_36`
13×	`associate-*r/_binary64_20`
11×	`log-rec_binary64_166`
10×	`distribute-lft1-in_binary64_33`
8×	`exp-sqrt_binary64_131` `cube-unmult_binary64_115` `/-rgt-identity_binary64_69` `distribute-lft-neg-in_binary64_35`
6×	`exp-sum_binary64_124` `remove-double-div_binary64_54` `associate-+l+_binary64_11`
5×	`associate-+r+_binary64_10`
4×	`pow-base-1_binary64_138` `prod-exp_binary64_127` `+-commutative_binary64_8`
3×	`div-sub_binary64_83` `count-2_binary64_26`
2×	`rem-log-exp_binary64_119` `rem-square-sqrt_binary64_90` `neg-mul-1_binary64_74` `mul0-lft_binary64_60` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55`
1×	`exp-lft-cube_binary64_134` `exp-diff_binary64_126` `1-exp_binary64_122` `exp-1-e_binary64_121` `sqr-abs_binary64_93` `unsub-neg_binary64_72` `div0_binary64_59` `lft-mult-inverse_binary64_56`
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` `unpow2_binary64_143` `unpow1/2_binary64_142` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-cbrt_binary64_132` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `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-neg_binary64_92` `neg-sub0_binary64_73` `mul-1-neg_binary64_70` `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` `+-inverses_binary64_57` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `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` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37` `distribute-lft-in_binary64_27` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--l+_binary64_15` `associate--r+_binary64_14` `associate-+l-_binary64_13` `associate-+r-_binary64_12`

Counts

56 → 63

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	860
1	133	697
2	360	697
3	691	697
4	861	697
5	1559	697
6	2526	697

prune71.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	64	5	69

Error

0.0b

Counts

69 → 5

Compiler

Compiled 971 to 769 computations (20.8% saved)

regimes420.0ms (10.4%)

Accuracy

Total 0.4b remaining (99.7%)

Threshold costs 0.4b (99.7%)

Compiler

Compiled 3786 to 3153 computations (16.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3× *-commutative_binary64_9

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 1-exp_binary64_122 exp-1-e_binary64_121 exp-0_binary64_120 sqr-abs_binary64_93 sqr-neg_binary64_92 neg-mul-1_binary64_74 neg-sub0_binary64_73 unsub-neg_binary64_72 sub-neg_binary64_71 mul-1-neg_binary64_70 /-rgt-identity_binary64_69 *-rgt-identity_binary64_68 *-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 cancel-sign-sub-inv_binary64_44 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 distribute-rgt-neg-out_binary64_38 distribute-lft-neg-out_binary64_37 distribute-rgt-neg-in_binary64_36 distribute-lft-neg-in_binary64_35 +-commutative_binary64_8

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	14	21

Proof

(* f64 (cbrt f64 (sqrt f64 2)) (* f64 (fabs f64 h0) (pow f64 (sqrt f64 2) (* f64 2 1/3))))

end0.0ms (0%)

sample1.4s (34%)

Algorithm

1×

intervals

Results

182.0ms	8000×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 869 to 738 computations (15.1% saved)

Details

analyze5.0ms (0.1%)

sample12.0ms (0.3%)

simplify148.0ms (3.7%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite50.0ms (1.2%)

series87.0ms (2.1%)

simplify173.0ms (4.3%)

prune77.0ms (1.9%)

localize4.0ms (0.1%)

rewrite25.0ms (0.6%)

series51.0ms (1.3%)

simplify371.0ms (9.2%)

prune18.0ms (0.5%)

localize7.0ms (0.2%)

rewrite92.0ms (2.3%)

series184.0ms (4.6%)

simplify356.0ms (8.8%)

prune102.0ms (2.5%)

localize6.0ms (0.1%)

rewrite82.0ms (2%)

series112.0ms (2.8%)

simplify203.0ms (5%)

prune71.0ms (1.8%)

regimes420.0ms (10.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (34%)

Profiling