Details

analyze261.0ms (4.1%)

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
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
32.8%	67.1%	0.1%	9
43.7%	43.7%	12.6%	10
46.8%	40.6%	12.6%	11
52.7%	34.7%	12.6%	12
58.5%	22.6%	18.9%	13
60.5%	20.7%	18.9%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample16.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
0.0ms	15×	body	128	invalid

Compiler

Compiled 15 to 16 computations (-6.7% saved)

simplify148.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64_9`
1×	`associate-l_binary64_19` `associate-r_binary64_18` `+-commutative_binary64_8`
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`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	13	10

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 2

Compiler

Compiled 21 to 18 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (.f64 (.f64 y z) z))
0.2b	(.f64 (.f64 y z) z)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117`
3×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `add-cube-cbrt_binary64_113` `cbrt-unprod_binary64_111` `add-sqr-sqrt_binary64_100` `-un-lft-identity_binary64_78` `associate-r*_binary64_18`
1×	`associate-l_binary64_19` `*-commutative_binary64_9` `sum-log_binary64_169` `flip3-+_binary64_81` `flip-+_binary64_52` `+-commutative_binary64_8`

Counts

2 → 29

Calls

2 calls:

6.0ms	(.f64 (.f64 y z) z)
3.0ms	(+.f64 x (.f64 (.f64 y z) z))

Compiler

Compiled 398 to 108 computations (72.9% saved)

series256.0ms (4.1%)

Error

0.1b

Counts

2 → 24

Calls

2 calls:

151.0ms	(+.f64 x (.f64 (.f64 y z) z))
91.0ms	(.f64 (.f64 y z) z)

Compiler

Compiled 373 to 330 computations (11.5% saved)

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-*l/_binary64_21`
623×	`associate-*r/_binary64_20`
182×	`distribute-rgt-in_binary64_28`
169×	`distribute-lft-in_binary64_27`
146×	`*-commutative_binary64_9`
121×	`distribute-rgt-neg-in_binary64_36`
118×	`associate-l_binary64_19`
116×	`times-frac_binary64_84`
114×	`unswap-sqr_binary64_46`
100×	`distribute-lft-neg-in_binary64_35`
94×	`associate-r_binary64_18`
89×	`cancel-sign-sub-inv_binary64_44`
63×	`associate-/r*_binary64_22`
59×	`sqr-pow_binary64_50`
52×	`distribute-rgt-out_binary64_31` `associate-/l*_binary64_23`
47×	`associate-/r/_binary64_24`
33×	`sub-neg_binary64_71`
29×	`pow-sqr_binary64_51`
28×	`exp-prod_binary64_130`
27×	`log-prod_binary64_164`
25×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
24×	`cube-prod_binary64_106` `swap-sqr_binary64_45`
23×	`associate-+l-_binary64_13`
22×	`distribute-neg-frac_binary64_42`
21×	`associate-/l/_binary64_25`
20×	`associate-+r-_binary64_12`
17×	`distribute-rgt-out--_binary64_32` `associate--l-_binary64_16`
16×	`associate-+l+_binary64_11`
14×	`distribute-lft-neg-out_binary64_37`
13×	`+-commutative_binary64_8`
12×	`cube-div_binary64_107` `associate-+r+_binary64_10`
11×	`log-div_binary64_165` `exp-sqrt_binary64_131`
10×	`pow-plus_binary64_141` `*-rgt-identity_binary64_68`
9×	`unsub-neg_binary64_72`
8×	`distribute-lft-out_binary64_29`
7×	`unpow3_binary64_144`
6×	`log-pow_binary64_167`
5×	`*-lft-identity_binary64_67` `+-rgt-identity_binary64_63`
4×	`cube-mult_binary64_108` `distribute-lft-out--_binary64_30` `associate--r+_binary64_14`
3×	`sub0-neg_binary64_65` `count-2_binary64_26`
2×	`pow-base-1_binary64_138` `prod-exp_binary64_127` `cube-unmult_binary64_115` `difference-of-squares_binary64_47` `distribute-neg-in_binary64_39` `distribute-rgt-neg-out_binary64_38` `distribute-rgt1-in_binary64_34`
1×	`unpow2_binary64_143` `unpow1_binary64_136` `exp-lft-sqr_binary64_133` `exp-diff_binary64_126` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `rem-sqrt-square_binary64_91` `/-rgt-identity_binary64_69` `*-inverses_binary64_58` `associate--l+_binary64_15`
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-rec_binary64_166` `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` `div-exp_binary64_129` `rec-exp_binary64_128` `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-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` `div-sub_binary64_83` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `--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_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft1-in_binary64_33` `associate--r-_binary64_17`

Counts

53 → 127

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	60	534
1	163	510
2	571	510
3	1091	510

prune97.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	121	8	129

Error

0.0b

Counts

129 → 8

Compiler

Compiled 1912 to 373 computations (80.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (.f64 (.f64 y z) z)) (cbrt.f64 (.f64 (*.f64 y z) z)))
17.9b	(cbrt.f64 (.f64 z (.f64 z y)))
17.9b	(cbrt.f64 (.f64 (.f64 y z) z))
17.9b	(cbrt.f64 (.f64 (.f64 y z) z))

rewrite84.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

11×	`pow1_binary64_139`
10×	`add-sqr-sqrt_binary64_100`
9×	`pow1/3_binary64_160`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`cbrt-prod_binary64_109`
6×	`add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `swap-sqr_binary64_45` `associate-l_binary64_19` `associate-r_binary64_18`
2×	`pow-prod-down_binary64_149` `pow-prod-up_binary64_148` `pow-sqr_binary64_51`
1×	`pow2_binary64_159` `pow-plus_binary64_141` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `*-commutative_binary64_9`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 (.f64 y z) z)) (cbrt.f64 (.f64 (*.f64 y z) z)))
4.0ms	(cbrt.f64 (.f64 (.f64 y z) z))
4.0ms	(cbrt.f64 (.f64 (.f64 y z) z))
3.0ms	(cbrt.f64 (.f64 z (.f64 z y)))

Compiler

Compiled 1629 to 261 computations (84% saved)

series1.3s (20.8%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

397.0ms	(.f64 (cbrt.f64 (.f64 (.f64 y z) z)) (cbrt.f64 (.f64 (*.f64 y z) z)))
303.0ms	(cbrt.f64 (.f64 (.f64 y z) z))
293.0ms	(cbrt.f64 (.f64 (.f64 y z) z))
292.0ms	(cbrt.f64 (.f64 z (.f64 z y)))

Compiler

Compiled 1920 to 1297 computations (32.4% saved)

simplify626.0ms (9.9%)

Algorithm

1×	egg-herbie

Rules

395×	`associate-l_binary64_19`
387×	`distribute-rgt-in_binary64_28`
371×	`exp-prod_binary64_130`
323×	`associate-r_binary64_18`
315×	`distribute-lft-in_binary64_27`
285×	`cancel-sign-sub-inv_binary64_44`
199×	`unswap-sqr_binary64_46`
128×	`exp-sum_binary64_124`
119×	`div-sub_binary64_83`
111×	`unsub-neg_binary64_72` `sqr-pow_binary64_50`
106×	`distribute-neg-out_binary64_40`
102×	`log-prod_binary64_164`
95×	`distribute-rgt-neg-in_binary64_36`
91×	`distribute-lft-neg-in_binary64_35`
86×	`distribute-lft-out_binary64_29`
84×	`swap-sqr_binary64_45` `*-commutative_binary64_9`
82×	`distribute-rgt-out_binary64_31`
81×	`distribute-rgt-neg-out_binary64_38`
67×	`distribute-lft-neg-out_binary64_37`
65×	`cube-prod_binary64_106`
63×	`associate-*l/_binary64_21`
60×	`exp-diff_binary64_126` `sub-neg_binary64_71` `distribute-rgt-out--_binary64_32`
50×	`log-div_binary64_165`
47×	`exp-to-pow_binary64_140` `neg-sub0_binary64_73`
44×	`distribute-lft-out--_binary64_30`
42×	`times-frac_binary64_84`
40×	`pow-sqr_binary64_51`
38×	`exp-sqrt_binary64_131`
37×	`neg-mul-1_binary64_74`
35×	`exp-lft-sqr_binary64_133` `distribute-neg-frac_binary64_42`
30×	`*-rgt-identity_binary64_68`
29×	`cube-div_binary64_107`
28×	`associate-*r/_binary64_20`
26×	`associate-/r*_binary64_22`
24×	`*-lft-identity_binary64_67` `distribute-neg-in_binary64_39`
22×	`exp-neg_binary64_125`
20×	`distribute-frac-neg_binary64_41`
18×	`log-pow_binary64_167`
17×	`pow-plus_binary64_141` `associate-/l*_binary64_23`
14×	`unpow1/3_binary64_145`
13×	`+-commutative_binary64_8`
12×	`cube-unmult_binary64_115` `associate-+r-_binary64_12`
11×	`associate-+l-_binary64_13`
10×	`associate-/r/_binary64_24` `associate-+r+_binary64_10`
8×	`associate--l+_binary64_15` `associate--r+_binary64_14` `associate-+l+_binary64_11`
7×	`log-rec_binary64_166` `/-rgt-identity_binary64_69` `remove-double-neg_binary64_66` `distribute-rgt1-in_binary64_34`
6×	`count-2_binary64_26` `associate-/l/_binary64_25`
5×	`rem-sqrt-square_binary64_91` `+-rgt-identity_binary64_63` `mul0-lft_binary64_60`
4×	`unpow3_binary64_144` `unpow2_binary64_143` `sub0-neg_binary64_65` `associate--r-_binary64_17` `associate--l-_binary64_16`
3×	`unpow1_binary64_136` `rem-3cbrt-lft_binary64_103` `mul0-rgt_binary64_61`
2×	`cube-mult_binary64_108` `--rgt-identity_binary64_64` `cancel-sign-sub_binary64_43`
1×	`pow-base-1_binary64_138` `prod-exp_binary64_127` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `rem-3cbrt-rft_binary64_104` `rem-square-sqrt_binary64_90` `*-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` `pow-base-0_binary64_162` `unpow1/2_binary64_142` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `div-exp_binary64_129` `rec-exp_binary64_128` `e-exp-1_binary64_123` `exp-0_binary64_120` `cube-neg_binary64_105` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `mul-1-neg_binary64_70` `+-lft-identity_binary64_62` `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` `difference-of-squares_binary64_47` `distribute-lft1-in_binary64_33`

Counts

82 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1330
1	236	1258
2	622	1142
3	2117	1000

prune210.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	194	8	202

Error

0.0b

Counts

202 → 8

Compiler

Compiled 5514 to 1396 computations (74.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)

rewrite85.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`cbrt-prod_binary64_109`
23×	`add-sqr-sqrt_binary64_100`
15×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`pow1_binary64_139`
9×	`pow1/3_binary64_160`
6×	`add-exp-log_binary64_116` `swap-sqr_binary64_45` `associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114` `unswap-sqr_binary64_46`
2×	`pow-prod-down_binary64_149` `pow-prod-up_binary64_148` `pow-sqr_binary64_51`
1×	`pow2_binary64_159` `pow-plus_binary64_141` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

Compiler

Compiled 1378 to 364 computations (73.6% saved)

series491.0ms (7.8%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

160.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
107.0ms	(cbrt.f64 z)
106.0ms	(cbrt.f64 z)
105.0ms	(cbrt.f64 z)

Compiler

Compiled 591 to 406 computations (31.3% saved)

simplify324.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

545×	`log-prod_binary64_164`
427×	`log-div_binary64_165`
416×	`associate-/l*_binary64_23`
347×	`associate-l_binary64_19`
293×	`associate-/r*_binary64_22`
231×	`associate-r_binary64_18`
203×	`*-commutative_binary64_9`
184×	`associate-/r/_binary64_24`
150×	`distribute-rgt-neg-in_binary64_36`
144×	`distribute-lft-neg-in_binary64_35`
140×	`exp-prod_binary64_130`
128×	`distribute-rgt-in_binary64_28`
123×	`unswap-sqr_binary64_46`
112×	`cube-prod_binary64_106`
95×	`distribute-lft-in_binary64_27`
86×	`swap-sqr_binary64_45`
80×	`associate-/l/_binary64_25`
77×	`sqr-pow_binary64_50`
55×	`log-pow_binary64_167` `distribute-rgt-out_binary64_31`
52×	`times-frac_binary64_84`
47×	`cancel-sign-sub-inv_binary64_44`
42×	`associate-+l+_binary64_11`
39×	`associate-+r+_binary64_10`
38×	`associate-*l/_binary64_21`
37×	`pow-sqr_binary64_51`
30×	`distribute-lft-out_binary64_29`
29×	`cube-div_binary64_107`
28×	`distribute-neg-frac_binary64_42`
24×	`log-rec_binary64_166` `*-rgt-identity_binary64_68`
23×	`*-lft-identity_binary64_67`
22×	`pow-plus_binary64_141`
21×	`associate-*r/_binary64_20`
19×	`exp-sqrt_binary64_131`
18×	`rem-sqrt-square_binary64_91`
15×	`cube-unmult_binary64_115`
13×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
12×	`associate-+l-_binary64_13`
9×	`exp-lft-sqr_binary64_133` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37`
8×	`distribute-rgt1-in_binary64_34` `count-2_binary64_26`
6×	`unpow3_binary64_144` `associate--l-_binary64_16` `associate--l+_binary64_15`
5×	`associate-+r-_binary64_12` `+-commutative_binary64_8`
4×	`div-exp_binary64_129` `prod-exp_binary64_127` `distribute-rgt-out--_binary64_32`
3×	`unpow1/3_binary64_145` `unpow2_binary64_143` `sub-neg_binary64_71` `distribute-lft-out--_binary64_30`
2×	`unpow1_binary64_136` `rec-exp_binary64_128` `exp-sum_binary64_124` `cube-mult_binary64_108` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `/-rgt-identity_binary64_69` `distribute-lft1-in_binary64_33`
1×	`pow-base-1_binary64_138` `exp-diff_binary64_126` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `rem-3cbrt-rft_binary64_104` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `mul0-lft_binary64_60` `*-inverses_binary64_58` `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` `log-E_binary64_168` `pow-base-0_binary64_162` `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-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `div-sub_binary64_83` `unsub-neg_binary64_72` `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` `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` `difference-of-squares_binary64_47` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-in_binary64_39` `associate--r-_binary64_17` `associate--r+_binary64_14`

Counts

85 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	718
1	97	656
2	345	636
3	1343	633
4	4059	633

prune87.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	82	9	91

Error

Counts

91 → 9

Compiler

Compiled 1678 to 506 computations (69.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 z)
0.6b	(cbrt.f64 (cbrt.f64 z))
0.7b	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))

rewrite64.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

16×	`cbrt-prod_binary64_109`
8×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`pow1/3_binary64_160` `pow1_binary64_139` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`

Counts

4 → 45

Calls

4 calls:

4.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
2.0ms	(cbrt.f64 (cbrt.f64 z))
1.0ms	(cbrt.f64 z)
1.0ms	(cbrt.f64 z)

Compiler

Compiled 1206 to 279 computations (76.9% saved)

series572.0ms (9.1%)

Error

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
140.0ms	(cbrt.f64 (cbrt.f64 z))
132.0ms	(cbrt.f64 z)
119.0ms	(cbrt.f64 z)

Compiler

Compiled 873 to 518 computations (40.7% saved)

simplify143.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

495×	`associate-+l+_binary64_11`
474×	`unswap-sqr_binary64_46`
459×	`distribute-rgt-in_binary64_28`
448×	`distribute-lft-in_binary64_27`
296×	`times-frac_binary64_84`
215×	`associate-l_binary64_19`
209×	`log-prod_binary64_164`
174×	`distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35`
167×	`associate-r_binary64_18`
162×	`associate-*l/_binary64_21`
147×	`sqr-pow_binary64_50`
119×	`*-commutative_binary64_9`
111×	`associate-/l*_binary64_23`
106×	`associate-*r/_binary64_20`
96×	`associate-/l/_binary64_25`
93×	`pow-sqr_binary64_51`
90×	`associate-/r/_binary64_24`
60×	`associate-/r*_binary64_22`
52×	`cancel-sign-sub-inv_binary64_44` `distribute-rgt-out_binary64_31`
50×	`pow-plus_binary64_141`
46×	`swap-sqr_binary64_45`
35×	`cube-prod_binary64_106`
34×	`log-pow_binary64_167`
33×	`cube-unmult_binary64_115`
28×	`neg-sub0_binary64_73`
27×	`neg-mul-1_binary64_74`
20×	`count-2_binary64_26`
16×	`exp-prod_binary64_130`
15×	`distribute-lft-out_binary64_29`
13×	`rem-sqrt-square_binary64_91`
12×	`sub-neg_binary64_71`
9×	`distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37`
8×	`distribute-rgt1-in_binary64_34`
5×	`unpow3_binary64_144` `/-rgt-identity_binary64_69` `+-commutative_binary64_8`
4×	`unpow1/3_binary64_145`
3×	`rem-3cbrt-lft_binary64_103` `associate-+r+_binary64_10`
2×	`unpow2_binary64_143` `unpow1_binary64_136` `distribute-lft1-in_binary64_33`
1×	`div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `1-exp_binary64_122` `cube-mult_binary64_108` `rem-cbrt-cube_binary64_102` `mul-1-neg_binary64_70` `-rgt-identity_binary64_68` `-lft-identity_binary64_67` `+-rgt-identity_binary64_63` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `associate-+l-_binary64_13` `associate-+r-_binary64_12`
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-rec_binary64_166` `log-div_binary64_165` `pow-base-0_binary64_162` `unpow1/2_binary64_142` `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` `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-div_binary64_107` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `rem-square-sqrt_binary64_90` `div-sub_binary64_83` `unsub-neg_binary64_72` `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` `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-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39` `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`

Counts

57 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	468
1	86	458
2	229	458
3	963	445
4	1929	437

prune50.0ms (0.8%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	38	9	47

Error

Counts

47 → 9

Compiler

Compiled 1039 to 318 computations (69.4% saved)

regimes301.0ms (4.8%)

Accuracy

Total 0.1b remaining (89%)

Threshold costs 0.1b (89%)

Compiler

Compiled 2735 to 1705 computations (37.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64_9`
1×	`+-commutative_binary64_8`
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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	10	10

Proof

(+ f64 h0 (=> (* f64 (* f64 h1 h2) h2)))
*-commutative_binary64_9 =>
(+ f64 h0 (* f64 h2 (* f64 h1 h2)))

end0.0ms (0%)

sample981.0ms (15.5%)

Algorithm

1×

intervals

Results

200.0ms	8000×	body	128	valid
15.0ms	672×	body	128	invalid

Compiler

Compiled 556 to 349 computations (37.2% saved)

Details

analyze261.0ms (4.1%)

sample16.0ms (0.3%)

simplify148.0ms (2.3%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

rewrite34.0ms (0.5%)

series256.0ms (4.1%)

simplify116.0ms (1.8%)

prune97.0ms (1.5%)

localize15.0ms (0.2%)

rewrite84.0ms (1.3%)

series1.3s (20.8%)

simplify626.0ms (9.9%)

prune210.0ms (3.3%)

localize11.0ms (0.2%)

rewrite85.0ms (1.4%)

series491.0ms (7.8%)

simplify324.0ms (5.1%)

prune87.0ms (1.4%)

localize15.0ms (0.2%)

rewrite64.0ms (1%)

series572.0ms (9.1%)

simplify143.0ms (2.3%)

prune50.0ms (0.8%)

regimes301.0ms (4.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample981.0ms (15.5%)

Profiling