Details

analyze2.0s (3.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	76.4%	4.9%	9
18.7%	76.4%	4.9%	10
21.8%	72.5%	5.7%	11
21.8%	69.8%	8.4%	12
32.7%	46.6%	20.7%	13
32.7%	46.6%	20.7%	14

Compiler

Compiled 20 to 20 computations (0% saved)

sample66.0ms (0.1%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
15.0ms	142×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify230.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-out--_binary64_32`
338×	`associate-l_binary64_19`
272×	`distribute-rgt-neg-in_binary64_36`
246×	`associate-r_binary64_18`
238×	`associate-/l*_binary64_23`
237×	`div-sub_binary64_83`
225×	`distribute-lft-neg-in_binary64_35`
196×	`unswap-sqr_binary64_46`
190×	`times-frac_binary64_84`
188×	`associate-*l/_binary64_21`
157×	`associate-*r/_binary64_20`
152×	`distribute-neg-frac_binary64_42`
134×	`cancel-sign-sub-inv_binary64_44`
127×	`swap-sqr_binary64_45`
126×	`associate-/r*_binary64_22`
120×	`associate-/l/_binary64_25`
104×	`cube-prod_binary64_106`
102×	`distribute-rgt-neg-out_binary64_38`
101×	`associate-/r/_binary64_24`
100×	`neg-mul-1_binary64_74` `distribute-lft-neg-out_binary64_37`
97×	`unsub-neg_binary64_72`
94×	`neg-sub0_binary64_73`
82×	`sub-neg_binary64_71`
77×	`sqr-pow_binary64_50`
73×	`distribute-rgt-out_binary64_31`
66×	`exp-prod_binary64_130`
51×	`cube-div_binary64_107`
49×	`distribute-rgt1-in_binary64_34`
45×	`pow-sqr_binary64_51`
44×	`difference-of-squares_binary64_47`
43×	`distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
41×	`distribute-frac-neg_binary64_41` `*-commutative_binary64_9`
38×	`distribute-neg-out_binary64_40`
34×	`pow-plus_binary64_141`
27×	`distribute-neg-in_binary64_39`
26×	`*-rgt-identity_binary64_68`
23×	`associate-+r+_binary64_10` `+-commutative_binary64_8`
21×	`div0_binary64_59`
20×	`*-lft-identity_binary64_67` `mul0-rgt_binary64_61` `mul0-lft_binary64_60`
18×	`+-rgt-identity_binary64_63`
14×	`distribute-lft-out_binary64_29`
13×	`unpow3_binary64_144` `distribute-lft1-in_binary64_33` `associate-+l+_binary64_11`
12×	`cube-unmult_binary64_115`
11×	`/-rgt-identity_binary64_69` `difference-of-sqr--1_binary64_49`
10×	`cube-mult_binary64_108` `associate--r+_binary64_14`
9×	`div-exp_binary64_129` `prod-exp_binary64_127`
7×	`--rgt-identity_binary64_64`
6×	`associate-+l-_binary64_13`
5×	`+-lft-identity_binary64_62` `+-inverses_binary64_57`
4×	`remove-double-neg_binary64_66` `sub0-neg_binary64_65` `difference-of-sqr-1_binary64_48` `distribute-lft-out--_binary64_30`
3×	`rec-exp_binary64_128` `associate-+r-_binary64_12`
2×	`unpow2_binary64_143` `unpow1_binary64_136` `exp-sum_binary64_124` `count-2_binary64_26`
1×	`pow-base-1_binary64_138` `exp-lft-sqr_binary64_133` `exp-sqrt_binary64_131` `1-exp_binary64_122` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `cancel-sign-sub_binary64_43` `associate--r-_binary64_17` `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-pow_binary64_167` `log-rec_binary64_166` `log-div_binary64_165` `log-prod_binary64_164` `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-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `rem-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `lft-mult-inverse_binary64_56` `associate--l-_binary64_16`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	33	29
2	73	29
3	154	29
4	536	29
5	2206	29
6	3094	29

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

10.7b

Counts

1 → 1

Compiler

Compiled 19 to 19 computations (0% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 t l) 2)
0.3b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.4b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite310.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

10.6b

Rules

143×	`add-sqr-sqrt_binary64_100`
108×	`times-frac_binary64_84`
98×	`*-un-lft-identity_binary64_78`
70×	`difference-of-squares_binary64_47`
49×	`add-cube-cbrt_binary64_113`
48×	`sqrt-prod_binary64_94`
41×	`unpow-prod-down_binary64_157`
15×	`unpow2_binary64_143` `sqr-pow_binary64_50`
14×	`associate-/l*_binary64_23`
9×	`add-exp-log_binary64_116`
7×	`distribute-lft-out--_binary64_30`
6×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`div-inv_binary64_75` `associate-/r*_binary64_22` `pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `associate-/l/_binary64_25` `pow-exp_binary64_146`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `asin-acos_binary64_258` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 173

Calls

4 calls:

21.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(pow.f64 (/.f64 t l) 2)
0.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))

Compiler

Compiled 6194 to 4307 computations (30.5% saved)

series1.2s (2.3%)

Error

1.5b

Counts

4 → 71

Calls

4 calls:

526.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
400.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
58.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
40.0ms	(pow.f64 (/.f64 t l) 2)

Compiler

Compiled 10085 to 8670 computations (14% saved)

simplify2.0s (4%)

Algorithm

1×	egg-herbie

Rules

215×	`associate-l_binary64_19`
207×	`associate-r_binary64_18`
198×	`associate-/l*_binary64_23`
193×	`associate-+r+_binary64_10`
189×	`times-frac_binary64_84`
187×	`associate-*r/_binary64_20`
170×	`associate-/r*_binary64_22`
161×	`associate-*l/_binary64_21`
158×	`+-commutative_binary64_8`
148×	`*-commutative_binary64_9`
140×	`associate-+l+_binary64_11`
93×	`sqr-pow_binary64_50`
84×	`sub-neg_binary64_71`
77×	`associate-/l/_binary64_25`
76×	`neg-mul-1_binary64_74`
70×	`div-sub_binary64_83` `associate--l+_binary64_15`
62×	`associate--r+_binary64_14`
60×	`cancel-sign-sub-inv_binary64_44`
47×	`pow-plus_binary64_141`
43×	`associate-/r/_binary64_24`
39×	`distribute-rgt-in_binary64_28`
35×	`unswap-sqr_binary64_46` `distribute-lft-in_binary64_27`
29×	`unpow2_binary64_143` `cube-prod_binary64_106` `neg-sub0_binary64_73` `distribute-rgt-neg-in_binary64_36`
27×	`unpow1_binary64_136`
24×	`pow-sqr_binary64_51`
23×	`rem-sqrt-square_binary64_91` `distribute-neg-in_binary64_39`
21×	`log-prod_binary64_164` `distribute-lft-neg-in_binary64_35`
20×	`distribute-rgt-out_binary64_31`
19×	`cube-div_binary64_107`
17×	`log-pow_binary64_167` `/-rgt-identity_binary64_69`
16×	`div-exp_binary64_129` `prod-exp_binary64_127`
15×	`log-div_binary64_165`
13×	`cube-unmult_binary64_115`
9×	`distribute-neg-frac_binary64_42`
8×	`unpow3_binary64_144` `exp-prod_binary64_130` `swap-sqr_binary64_45`
7×	`mul-1-neg_binary64_70` `distribute-rgt-out--_binary64_32`
6×	`pow-base-1_binary64_138` `*-lft-identity_binary64_67` `distribute-lft-neg-out_binary64_37`
5×	`cube-mult_binary64_108` `difference-of-squares_binary64_47`
4×	`rec-exp_binary64_128` `rem-square-sqrt_binary64_90`
3×	`*-rgt-identity_binary64_68`
2×	`exp-sum_binary64_124` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `distribute-rgt1-in_binary64_34` `distribute-lft-out_binary64_29`
1×	`log-rec_binary64_166` `exp-diff_binary64_126` `1-exp_binary64_122` `rem-log-exp_binary64_119` `unsub-neg_binary64_72` `*-inverses_binary64_58` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `associate--r-_binary64_17` `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` `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-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `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` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt-neg-out_binary64_38` `distribute-lft1-in_binary64_33` `associate--l-_binary64_16`

Counts

244 → 489

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	587	13451
1	1351	11336
2	4727	11297

prune732.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	484	5	489
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	484	6	490

Error

1.1b

Counts

490 → 6

Compiler

Compiled 19932 to 12799 computations (35.8% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.8b	(cbrt.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))

rewrite608.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

184×	`add-sqr-sqrt_binary64_100`
147×	`times-frac_binary64_84`
144×	`sqrt-prod_binary64_94`
121×	`*-un-lft-identity_binary64_78`
90×	`difference-of-squares_binary64_47`
58×	`add-cube-cbrt_binary64_113`
36×	`unpow-prod-down_binary64_157`
18×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`distribute-lft-out--_binary64_30`
7×	`pow1_binary64_139`
6×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52`
1×	`pow1/3_binary64_160` `cbrt-prod_binary64_109` `cube-unmult_binary64_115` `rem-cbrt-cube_binary64_102`

Counts

4 → 190

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
14.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms	(cbrt.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))

Compiler

Compiled 15331 to 10817 computations (29.4% saved)

series2.2s (4.4%)

Error

1.1b

Counts

4 → 90

Calls

4 calls:

589.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
581.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
546.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
89.0ms	(cbrt.f64 (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))))

Compiler

Compiled 27687 to 22605 computations (18.4% saved)

simplify4.6s (9%)

Algorithm

1×	egg-herbie

Rules

321×	`cancel-sign-sub-inv_binary64_44`
200×	`unswap-sqr_binary64_46`
172×	`associate-+r+_binary64_10`
168×	`sub-neg_binary64_71`
158×	`associate-r_binary64_18`
156×	`associate-l_binary64_19`
149×	`times-frac_binary64_84`
146×	`associate-/l*_binary64_23`
137×	`associate-*r/_binary64_20`
129×	`associate-/r*_binary64_22`
126×	`distribute-rgt-neg-in_binary64_36`
122×	`+-commutative_binary64_8`
119×	`*-commutative_binary64_9`
114×	`associate-+l+_binary64_11`
105×	`distribute-neg-frac_binary64_42`
104×	`associate-*l/_binary64_21`
99×	`distribute-lft-neg-in_binary64_35`
97×	`distribute-neg-in_binary64_39`
93×	`sqr-pow_binary64_50`
84×	`distribute-rgt-out_binary64_31`
70×	`neg-sub0_binary64_73`
64×	`neg-mul-1_binary64_74`
53×	`associate-/l/_binary64_25`
48×	`pow-sqr_binary64_51`
41×	`div-sub_binary64_83`
40×	`associate--l+_binary64_15`
36×	`associate--r+_binary64_14`
28×	`associate-/r/_binary64_24`
24×	`distribute-lft-neg-out_binary64_37`
23×	`/-rgt-identity_binary64_69`
20×	`distribute-rgt-out--_binary64_32`
18×	`pow-plus_binary64_141` `cube-prod_binary64_106`
17×	`unsub-neg_binary64_72`
16×	`div-exp_binary64_129` `prod-exp_binary64_127`
15×	`cube-div_binary64_107` `*-rgt-identity_binary64_68`
14×	`rem-sqrt-square_binary64_91`
9×	`swap-sqr_binary64_45`
8×	`unpow3_binary64_144` `unpow2_binary64_143` `unpow1_binary64_136` `mul-1-neg_binary64_70` `*-lft-identity_binary64_67` `difference-of-squares_binary64_47`
7×	`cube-mult_binary64_108`
6×	`distribute-rgt1-in_binary64_34`
5×	`cube-unmult_binary64_115` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
4×	`rec-exp_binary64_128`
3×	`pow-base-1_binary64_138` `distribute-rgt-neg-out_binary64_38`
2×	`rem-square-sqrt_binary64_90` `distribute-lft1-in_binary64_33` `distribute-lft-out_binary64_29`
1×	`1-exp_binary64_122` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `--rgt-identity_binary64_64` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `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-pow_binary64_167` `log-rec_binary64_166` `log-div_binary64_165` `log-prod_binary64_164` `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-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `exp-prod_binary64_130` `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-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `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

280 → 709

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	446	22827
1	1022	18761
2	3534	18113

prune4.1s (8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	705	4	709
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	706	9	715

Error

1.1b

Counts

715 → 9

Compiler

Compiled 67251 to 45658 computations (32.1% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

8.8b	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite698.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

185×	`add-sqr-sqrt_binary64_100`
147×	`times-frac_binary64_84`
144×	`sqrt-prod_binary64_94`
122×	`*-un-lft-identity_binary64_78`
90×	`difference-of-squares_binary64_47`
59×	`add-cube-cbrt_binary64_113`
36×	`unpow-prod-down_binary64_157`
18×	`unpow2_binary64_143` `sqr-pow_binary64_50`
9×	`distribute-lft-out--_binary64_30`
7×	`pow1_binary64_139`
6×	`associate-/r/_binary64_24` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52` `cbrt-prod_binary64_109`
1×	`pow1/3_binary64_160`

Counts

4 → 191

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
16.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
1.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 15683 to 11181 computations (28.7% saved)

series2.7s (5.2%)

Error

1.1b

Counts

4 → 90

Calls

4 calls:

675.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
556.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
550.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
418.0ms	(cbrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 29637 to 24171 computations (18.4% saved)

simplify4.5s (8.8%)

Algorithm

1×	egg-herbie

Rules

321×	`cancel-sign-sub-inv_binary64_44`
202×	`unswap-sqr_binary64_46`
171×	`associate-+r+_binary64_10`
168×	`sub-neg_binary64_71`
157×	`associate-r_binary64_18`
156×	`associate-l_binary64_19`
149×	`times-frac_binary64_84`
146×	`associate-/l*_binary64_23`
137×	`associate-*r/_binary64_20`
129×	`associate-/r*_binary64_22`
126×	`distribute-rgt-neg-in_binary64_36`
122×	`*-commutative_binary64_9`
116×	`+-commutative_binary64_8`
114×	`associate-+l+_binary64_11`
105×	`distribute-neg-frac_binary64_42`
104×	`associate-*l/_binary64_21`
99×	`distribute-lft-neg-in_binary64_35`
97×	`distribute-neg-in_binary64_39`
96×	`sqr-pow_binary64_50`
84×	`distribute-rgt-out_binary64_31`
70×	`neg-sub0_binary64_73`
64×	`neg-mul-1_binary64_74`
53×	`associate-/l/_binary64_25`
51×	`pow-sqr_binary64_51`
41×	`div-sub_binary64_83`
40×	`associate--l+_binary64_15`
36×	`associate--r+_binary64_14`
28×	`associate-/r/_binary64_24`
24×	`distribute-lft-neg-out_binary64_37`
23×	`/-rgt-identity_binary64_69`
20×	`distribute-rgt-out--_binary64_32`
19×	`cube-prod_binary64_106`
18×	`pow-plus_binary64_141`
17×	`unsub-neg_binary64_72`
16×	`div-exp_binary64_129` `prod-exp_binary64_127`
15×	`cube-div_binary64_107` `rem-sqrt-square_binary64_91` `*-rgt-identity_binary64_68`
9×	`swap-sqr_binary64_45`
8×	`unpow3_binary64_144` `unpow2_binary64_143` `unpow1_binary64_136` `mul-1-neg_binary64_70` `*-lft-identity_binary64_67` `difference-of-squares_binary64_47`
7×	`cube-mult_binary64_108`
6×	`distribute-rgt1-in_binary64_34`
5×	`distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
4×	`rec-exp_binary64_128` `cube-unmult_binary64_115`
3×	`pow-base-1_binary64_138` `distribute-rgt-neg-out_binary64_38`
2×	`log-pow_binary64_167` `rem-square-sqrt_binary64_90` `distribute-lft1-in_binary64_33` `distribute-lft-out_binary64_29`
1×	`log-prod_binary64_164` `unpow1/3_binary64_145` `exp-prod_binary64_130` `1-exp_binary64_122` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `--rgt-identity_binary64_64` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `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` `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-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `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_63` `+-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` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

281 → 728

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	448	22934
1	1027	18900
2	3545	18223

prune5.0s (9.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	728	0	728
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	728	9	737

Error

1.1b

Counts

737 → 9

Compiler

Compiled 71893 to 49279 computations (31.5% saved)

localize22.0ms (0%)

Local error

Found 4 expressions with local error:

8.4b	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
10.0b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.8b	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))

rewrite418.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

129×	`add-sqr-sqrt_binary64_100`
99×	`sqrt-prod_binary64_94`
98×	`times-frac_binary64_84`
86×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
44×	`add-cube-cbrt_binary64_113`
27×	`unpow-prod-down_binary64_157`
13×	`sqr-pow_binary64_50`
12×	`cbrt-prod_binary64_109` `unpow2_binary64_143`
7×	`pow1_binary64_139`
6×	`distribute-lft-out--_binary64_30`
5×	`rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `associate-/r/_binary64_24`
3×	`cube-prod_binary64_106` `pow1/2_binary64_158` `sqrt-pow1_binary64_96`
2×	`sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52`
1×	`pow1/3_binary64_160` `unpow3_binary64_144` `cube-mult_binary64_108` `rem-cbrt-cube_binary64_102`

Counts

4 → 154

Calls

4 calls:

17.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
15.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
2.0ms	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))
1.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))

Compiler

Compiled 9864 to 7180 computations (27.2% saved)

series1.5s (3%)

Error

1.1b

Counts

4 → 76

Calls

4 calls:

522.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
520.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
114.0ms	(sqrt.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
67.0ms	(cbrt.f64 (pow.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) 3))

Compiler

Compiled 19302 to 16248 computations (15.8% saved)

simplify3.1s (6.1%)

Algorithm

1×	egg-herbie

Rules

321×	`cancel-sign-sub-inv_binary64_44`
250×	`unswap-sqr_binary64_46`
173×	`associate-r_binary64_18`
172×	`associate-+r+_binary64_10`
171×	`associate-l_binary64_19`
168×	`sub-neg_binary64_71`
149×	`times-frac_binary64_84`
146×	`associate-/l*_binary64_23`
137×	`associate-*r/_binary64_20`
129×	`associate-/r*_binary64_22`
120×	`*-commutative_binary64_9` `+-commutative_binary64_8`
115×	`sqr-pow_binary64_50`
114×	`associate-+l+_binary64_11`
105×	`distribute-neg-frac_binary64_42`
104×	`associate-*l/_binary64_21`
70×	`neg-sub0_binary64_73`
64×	`neg-mul-1_binary64_74`
62×	`pow-sqr_binary64_51`
54×	`associate-/l/_binary64_25`
41×	`div-sub_binary64_83`
40×	`associate--l+_binary64_15`
36×	`associate--r+_binary64_14`
28×	`associate-/r/_binary64_24`
25×	`pow-plus_binary64_141` `distribute-rgt-neg-in_binary64_36`
24×	`rem-sqrt-square_binary64_91`
23×	`/-rgt-identity_binary64_69`
22×	`cube-prod_binary64_106`
19×	`distribute-rgt-out_binary64_31`
17×	`unsub-neg_binary64_72` `distribute-lft-neg-in_binary64_35`
16×	`div-exp_binary64_129` `prod-exp_binary64_127`
15×	`cube-div_binary64_107` `*-rgt-identity_binary64_68`
13×	`unpow3_binary64_144`
12×	`distribute-neg-in_binary64_39`
11×	`cube-mult_binary64_108`
9×	`swap-sqr_binary64_45`
8×	`unpow2_binary64_143` `unpow1_binary64_136` `mul-1-neg_binary64_70` `*-lft-identity_binary64_67` `difference-of-squares_binary64_47`
6×	`log-prod_binary64_164` `exp-prod_binary64_130` `distribute-lft-neg-out_binary64_37` `distribute-rgt-out--_binary64_32`
5×	`cube-unmult_binary64_115` `rem-cbrt-cube_binary64_102` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
4×	`rec-exp_binary64_128`
3×	`log-pow_binary64_167` `pow-base-1_binary64_138` `rem-square-sqrt_binary64_90`
2×	`distribute-lft-out_binary64_29`
1×	`1-exp_binary64_122` `rem-3cbrt-lft_binary64_103` `rem-cube-cbrt_binary64_101` `--rgt-identity_binary64_64` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-rgt1-in_binary64_34` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `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` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-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-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `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-lft1-in_binary64_33` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

230 → 557

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	472	17117
1	1054	14139
2	3674	14071

prune2.8s (5.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	556	1	557
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	557	9	566

Error

1.1b

Counts

566 → 9

Compiler

Compiled 43202 to 29761 computations (31.1% saved)

regimes4.8s (9.3%)

Accuracy

Total 0.5b remaining (42.8%)

Threshold costs 0.5b (42.8%)

Compiler

Compiled 96538 to 79075 computations (18.1% saved)

bsearch9.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64_9`
14×	`sub-neg_binary64_71` `+-commutative_binary64_8`
11×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
6×	`distribute-rgt-neg-in_binary64_36`
4×	`cancel-sign-sub-inv_binary64_44` `distribute-lft-neg-in_binary64_35`
2×	`distribute-lft-neg-out_binary64_37`
1×	`1-exp_binary64_122` `distribute-neg-frac_binary64_42` `distribute-rgt-neg-out_binary64_38`
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` `unsub-neg_binary64_72` `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_binary64_43` `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	38	120
1	63	120
2	93	120
3	114	120
4	127	120
5	130	120

Proof

(if real (<= f64 (/ f64 h0 h1) -1561628009969816519473507428179007671620869888963815024819955108888394126589952) (asin f64 (* f64 (sqrt f64 (- f64 1 (pow f64 (/ f64 h2 h3) 2))) (neg f64 (/ f64 (sqrt f64 1/2) (/ f64 h0 h1))))) (if real (<= f64 (/ f64 h0 h1) 2538593515635444948282853219064150300175131450914355177062400) (asin f64 (sqrt f64 (* f64 (/ f64 (- f64 1 (pow f64 (/ f64 h2 h3) 2)) (- f64 1 (* f64 (* f64 2 2) (pow f64 (/ f64 h0 h1) (* f64 2 2))))) (- f64 1 (* f64 2 (pow f64 (/ f64 h0 h1) 2)))))) (asin f64 (* f64 (sqrt f64 (- f64 1 (pow f64 (/ f64 h2 h3) 2))) (/ f64 (sqrt f64 1/2) (/ f64 h0 h1))))))

end0.0ms (0%)

sample7.6s (14.8%)

Algorithm

1×

intervals

Results

1.5s	8000×	body	128	valid
713.0ms	4733×	body	128	nan

Compiler

Compiled 5452 to 4479 computations (17.8% saved)

Details

analyze2.0s (3.8%)

sample66.0ms (0.1%)

simplify230.0ms (0.4%)

prune1.0ms (0%)

localize13.0ms (0%)

rewrite310.0ms (0.6%)

series1.2s (2.3%)

simplify2.0s (4%)

prune732.0ms (1.4%)

localize25.0ms (0%)

rewrite608.0ms (1.2%)

series2.2s (4.4%)

simplify4.6s (9%)

prune4.1s (8%)

localize20.0ms (0%)

rewrite698.0ms (1.4%)

series2.7s (5.2%)

simplify4.5s (8.8%)

prune5.0s (9.8%)

localize22.0ms (0%)

rewrite418.0ms (0.8%)

series1.5s (3%)

simplify3.1s (6.1%)

prune2.8s (5.4%)

regimes4.8s (9.3%)

bsearch9.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample7.6s (14.8%)

Profiling