Details

analyze1.7s (7%)

Algorithm

1×	search
2×	egg-herbie

Rules

591×	`associate-/r/_binary64_24`
531×	`associate-/l/_binary64_25`
297×	`associate-l_binary64_19`
268×	`associate-r_binary64_18`
230×	`cancel-sign-sub-inv_binary64_44`
219×	`associate-/l*_binary64_23`
206×	`distribute-neg-frac_binary64_42`
174×	`distribute-rgt-neg-in_binary64_36`
167×	`distribute-lft-neg-in_binary64_35`
159×	`associate-*l/_binary64_21`
153×	`*-commutative_binary64_9`
149×	`associate-*r/_binary64_20`
120×	`unswap-sqr_binary64_46`
114×	`div-sub_binary64_83`
108×	`sub-neg_binary64_71`
74×	`associate-/r*_binary64_22`
70×	`sqr-pow_binary64_50`
64×	`times-frac_binary64_84` `neg-mul-1_binary64_74` `neg-sub0_binary64_73`
46×	`distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37`
45×	`distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27`
30×	`pow-plus_binary64_141`
27×	`distribute-frac-neg_binary64_41`
25×	`+-commutative_binary64_8`
20×	`cube-unmult_binary64_115`
13×	`sub0-neg_binary64_65` `div0_binary64_59` `associate-+l-_binary64_13`
12×	`difference-of-sqr-1_binary64_48`
10×	`unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `rem-sqrt-square_binary64_91`
7×	`associate-+r-_binary64_12`
6×	`+-rgt-identity_binary64_63` `associate-+l+_binary64_11`
4×	`difference-of-sqr--1_binary64_49`
1×	`1-exp_binary64_122`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `log-div_binary64_165` `log-prod_binary64_164` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow3_binary64_144` `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-prod_binary64_130` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-mult_binary64_108` `cube-div_binary64_107` `cube-prod_binary64_106` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `rem-square-sqrt_binary64_90` `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` `--rgt-identity_binary64_64` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `*-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` `difference-of-squares_binary64_47` `swap-sqr_binary64_45` `cancel-sign-sub_binary64_43` `distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39` `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` `count-2_binary64_26` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--l+_binary64_15` `associate--r+_binary64_14` `associate-+r+_binary64_10`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	203
1	143	203
2	285	203
3	807	203
4	2655	203
5	4997	203
0	4	4
1	4	4

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)

sample61.0ms (0.3%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
15.0ms	170×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify55.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

525×	`associate-/r/_binary64_24`
484×	`unswap-sqr_binary64_46`
458×	`associate-/l/_binary64_25`
422×	`associate-*l/_binary64_21`
301×	`*-commutative_binary64_9`
297×	`cancel-sign-sub-inv_binary64_44` `associate-l_binary64_19`
260×	`associate-*r/_binary64_20`
253×	`distribute-rgt-neg-in_binary64_36`
218×	`div-sub_binary64_83`
215×	`associate-/l*_binary64_23`
205×	`neg-mul-1_binary64_74` `associate-r_binary64_18`
131×	`distribute-neg-frac_binary64_42`
108×	`associate-/r*_binary64_22`
103×	`times-frac_binary64_84`
83×	`distribute-lft-neg-in_binary64_35`
67×	`distribute-lft-neg-out_binary64_37`
66×	`sub-neg_binary64_71` `distribute-rgt-neg-out_binary64_38`
50×	`neg-sub0_binary64_73`
46×	`sqr-pow_binary64_50` `distribute-frac-neg_binary64_41` `distribute-rgt-in_binary64_28`
39×	`distribute-lft-in_binary64_27`
34×	`unsub-neg_binary64_72`
27×	`div0_binary64_59`
26×	`pow-plus_binary64_141`
22×	`cube-prod_binary64_106`
16×	`mul0-rgt_binary64_61` `distribute-neg-in_binary64_39`
14×	`rem-sqrt-square_binary64_91` `+-commutative_binary64_8`
10×	`cube-unmult_binary64_115`
9×	`mul0-lft_binary64_60`
8×	`unpow3_binary64_144`
7×	`associate-+l-_binary64_13`
6×	`unpow2_binary64_143` `pow-sqr_binary64_51` `difference-of-sqr--1_binary64_49`
5×	`sub0-neg_binary64_65`
4×	`unpow1_binary64_136` `cube-mult_binary64_108` `-rgt-identity_binary64_68` `-lft-identity_binary64_67` `difference-of-sqr-1_binary64_48`
3×	`--rgt-identity_binary64_64` `associate--r+_binary64_14`
2×	`unpow1/2_binary64_142` `swap-sqr_binary64_45` `associate-+l+_binary64_11` `associate-+r+_binary64_10`
1×	`1-exp_binary64_122` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `+-rgt-identity_binary64_63` `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` `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-prod_binary64_130` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-div_binary64_107` `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` `/-rgt-identity_binary64_69` `+-lft-identity_binary64_62` `*-inverses_binary64_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-squares_binary64_47` `cancel-sign-sub_binary64_43` `distribute-neg-out_binary64_40` `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` `count-2_binary64_26` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--l+_binary64_15`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	33	29
2	61	29
3	158	29
4	476	29
5	1619	29
6	3417	29
7	4797	29
8	4895	29

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

11.6b

Counts

1 → 1

Compiler

Compiled 19 to 19 computations (0% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 Om Omc) 2)
0.5b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.7b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.2b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite517.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

11.5b

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:

19.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms	(pow.f64 (/.f64 Om Omc) 2)
1.0ms	(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 4303 computations (30.5% saved)

series2.2s (9.4%)

Error

1.7b

Counts

4 → 63

Calls

4 calls:

942.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
880.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
162.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
115.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 5815 to 5190 computations (10.7% saved)

simplify262.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

236 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	335	9989
1	700	8463
2	1788	8166
3	4937	8166
4	4955	8166

prune352.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Error

0.8b

Counts

182 → 7

Compiler

Compiled 5223 to 3498 computations (33% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
7.4b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
10.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite583.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

128×	`sqrt-prod_binary64_94`
104×	`add-sqr-sqrt_binary64_100`
88×	`times-frac_binary64_84`
80×	`*-un-lft-identity_binary64_78`
44×	`add-cube-cbrt_binary64_113`
24×	`difference-of-squares_binary64_47`
10×	`sqrt-div_binary64_95`
8×	`pow1_binary64_139` `rem-sqrt-square_binary64_91`
6×	`distribute-lft-out_binary64_29` `distribute-lft-out--_binary64_30`
4×	`pow1/2_binary64_158` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-/r/_binary64_24`
2×	`div-inv_binary64_75`

Counts

4 → 140

Calls

4 calls:

19.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
13.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 7448 to 5106 computations (31.4% saved)

series2.2s (9.4%)

Error

0.8b

Counts

4 → 78

Calls

4 calls:

791.0ms	(sqrt.f64 (/.f64 (-.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
770.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
228.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
212.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 9422 to 7622 computations (19.1% saved)

simplify192.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

575×	`times-frac_binary64_84`
366×	`associate-/l*_binary64_23`
307×	`associate-*r/_binary64_20`
294×	`associate-/r*_binary64_22`
287×	`associate-*l/_binary64_21`
161×	`cancel-sign-sub-inv_binary64_44`
124×	`distribute-rgt-neg-in_binary64_36`
114×	`distribute-lft-neg-in_binary64_35`
98×	`distribute-neg-frac_binary64_42`
93×	`associate-/l/_binary64_25`
80×	`associate-r_binary64_18`
73×	`sub-neg_binary64_71`
67×	`*-commutative_binary64_9`
66×	`associate-l_binary64_19`
57×	`neg-sub0_binary64_73`
55×	`neg-mul-1_binary64_74` `sqr-pow_binary64_50`
47×	`unswap-sqr_binary64_46`
41×	`distribute-rgt-in_binary64_28`
40×	`+-commutative_binary64_8`
39×	`associate-/r/_binary64_24`
32×	`distribute-lft-in_binary64_27`
28×	`exp-prod_binary64_130`
21×	`exp-sum_binary64_124`
20×	`distribute-rgt-out_binary64_31`
16×	`div-sub_binary64_83`
15×	`cube-prod_binary64_106` `unsub-neg_binary64_72`
13×	`distribute-neg-in_binary64_39`
12×	`rem-sqrt-square_binary64_91`
11×	`log-prod_binary64_164` `distribute-rgt1-in_binary64_34`
10×	`distribute-lft-neg-out_binary64_37` `associate--r+_binary64_14` `associate-+l+_binary64_11`
9×	`cube-div_binary64_107` `associate--l+_binary64_15`
8×	`unpow3_binary64_144` `/-rgt-identity_binary64_69`
7×	`cube-mult_binary64_108` `*-rgt-identity_binary64_68` `swap-sqr_binary64_45` `distribute-rgt-out--_binary64_32`
6×	`exp-to-pow_binary64_140` `*-lft-identity_binary64_67` `distribute-lft-out_binary64_29` `associate-+r+_binary64_10`
5×	`unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `cube-unmult_binary64_115` `pow-sqr_binary64_51` `distribute-rgt-neg-out_binary64_38` `distribute-lft-out--_binary64_30`
4×	`log-pow_binary64_167` `log-div_binary64_165` `rem-square-sqrt_binary64_90` `associate-+r-_binary64_12`
3×	`exp-lft-sqr_binary64_133` `mul-1-neg_binary64_70`
2×	`exp-diff_binary64_126` `associate-+l-_binary64_13`
1×	`log-rec_binary64_166` `1-exp_binary64_122` `+-rgt-identity_binary64_63`
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` `pow-plus_binary64_141` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `*-inverses_binary64_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

218 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	296	8764
1	614	8304
2	1484	7746
3	4980	7746

prune400.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	129	7	136

Error

0.8b

Counts

136 → 7

Compiler

Compiled 6127 to 4155 computations (32.2% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.4b	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
10.8b	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite370.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

46×	`sqrt-prod_binary64_94`
34×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100`
26×	`times-frac_binary64_84`
22×	`add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139` `cbrt-prod_binary64_109` `distribute-lft-out_binary64_29`
5×	`sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `cbrt-div_binary64_110` `flip-+_binary64_52` `rem-sqrt-square_binary64_91`
2×	`pow1/3_binary64_160` `pow1/2_binary64_158` `sqrt-pow1_binary64_96` `associate-/r/_binary64_24`
1×	`div-inv_binary64_75`

Counts

4 → 84

Calls

4 calls:

16.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
4.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 5360 to 3800 computations (29.1% saved)

series1.9s (7.9%)

Error

0.8b

Counts

4 → 63

Calls

4 calls:

817.0ms	(sqrt.f64 (/.f64 (+.f64 1 (/.f64 Om Omc)) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
302.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
284.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
228.0ms	(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 9622 to 7728 computations (19.7% saved)

simplify156.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

631×	`times-frac_binary64_84`
406×	`associate-/l*_binary64_23`
302×	`associate-/r*_binary64_22`
296×	`associate-*l/_binary64_21`
290×	`associate-*r/_binary64_20`
123×	`cancel-sign-sub-inv_binary64_44`
90×	`distribute-rgt-neg-in_binary64_36`
85×	`associate-r_binary64_18`
82×	`distribute-lft-neg-in_binary64_35`
74×	`associate-/r/_binary64_24`
73×	`*-commutative_binary64_9`
70×	`associate-l_binary64_19`
62×	`sqr-pow_binary64_50`
59×	`unswap-sqr_binary64_46`
53×	`associate-/l/_binary64_25`
52×	`distribute-neg-frac_binary64_42`
46×	`sub-neg_binary64_71`
44×	`distribute-rgt-in_binary64_28`
40×	`distribute-lft-in_binary64_27`
36×	`exp-sum_binary64_124`
34×	`exp-prod_binary64_130` `+-commutative_binary64_8`
33×	`neg-sub0_binary64_73`
31×	`neg-mul-1_binary64_74`
16×	`cube-prod_binary64_106`
15×	`log-prod_binary64_164`
14×	`distribute-rgt-out_binary64_31`
12×	`log-pow_binary64_167` `unsub-neg_binary64_72` `distribute-lft-neg-out_binary64_37`
10×	`cube-div_binary64_107`
9×	`exp-diff_binary64_126` `div-sub_binary64_83` `distribute-rgt-neg-out_binary64_38` `distribute-rgt1-in_binary64_34` `associate--l+_binary64_15` `associate-+l+_binary64_11`
8×	`unpow3_binary64_144` `pow-sqr_binary64_51` `swap-sqr_binary64_45` `distribute-rgt-out--_binary64_32`
7×	`log-div_binary64_165` `cube-mult_binary64_108` `*-rgt-identity_binary64_68`
6×	`exp-to-pow_binary64_140` `rem-sqrt-square_binary64_91` `distribute-neg-in_binary64_39`
5×	`unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `cube-unmult_binary64_115` `*-lft-identity_binary64_67` `distribute-lft-out--_binary64_30`
4×	`associate-+l-_binary64_13` `associate-+r-_binary64_12` `associate-+r+_binary64_10`
3×	`unpow1/3_binary64_145` `exp-lft-sqr_binary64_133` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `remove-double-neg_binary64_66` `distribute-lft-out_binary64_29` `associate--r+_binary64_14`
2×	`associate--l-_binary64_16`
1×	`log-rec_binary64_166` `1-exp_binary64_122` `rem-3cbrt-lft_binary64_103` `+-rgt-identity_binary64_63` `cancel-sign-sub_binary64_43`
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` `pow-plus_binary64_141` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `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_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate--r-_binary64_17`

Counts

147 → 81

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	4962
1	508	4660
2	1337	4312
3	4998	4312
4	4958	4312

prune280.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	81	7	88

Error

0.8b

Counts

88 → 7

Compiler

Compiled 4760 to 3345 computations (29.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
1.5b	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
17.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
17.0b	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite857.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

145×	`cbrt-prod_binary64_109`
140×	`add-sqr-sqrt_binary64_100`
118×	`times-frac_binary64_84`
108×	`sqrt-prod_binary64_94`
95×	`*-un-lft-identity_binary64_78`
60×	`difference-of-squares_binary64_47`
53×	`add-cube-cbrt_binary64_113`
24×	`unpow-prod-down_binary64_157`
12×	`unpow2_binary64_143` `sqr-pow_binary64_50`
6×	`cbrt-div_binary64_110` `distribute-lft-out--_binary64_30`
5×	`pow1_binary64_139` `rem-sqrt-square_binary64_91`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`flip3-+_binary64_81` `flip-+_binary64_52`
2×	`pow1/3_binary64_160` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `div-inv_binary64_75` `asin-acos_binary64_258`

Counts

4 → 157

Calls

4 calls:

27.0ms	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
3.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms	(asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))

Compiler

Compiled 10007 to 7266 computations (27.4% saved)

series2.8s (11.8%)

Error

0.8b

Counts

4 → 60

Calls

4 calls:

1.6s	(sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
403.0ms	(asin.f64 (.f64 (fabs.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))))
282.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
276.0ms	(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

Compiler

Compiled 9654 to 8247 computations (14.6% saved)

simplify309.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

654×	`times-frac_binary64_84`
395×	`associate-/l*_binary64_23`
157×	`cancel-sign-sub-inv_binary64_44`
124×	`exp-prod_binary64_130`
112×	`unswap-sqr_binary64_46`
101×	`associate-/l/_binary64_25`
99×	`distribute-rgt-neg-in_binary64_36`
97×	`associate-/r/_binary64_24`
96×	`associate-r_binary64_18`
91×	`log-prod_binary64_164`
90×	`distribute-lft-neg-in_binary64_35`
86×	`sqr-pow_binary64_50`
84×	`distribute-rgt-in_binary64_28`
82×	`*-commutative_binary64_9`
81×	`sub-neg_binary64_71`
78×	`associate-l_binary64_19`
76×	`distribute-lft-in_binary64_27`
55×	`exp-sum_binary64_124`
53×	`neg-mul-1_binary64_74`
52×	`neg-sub0_binary64_73`
49×	`associate-/r*_binary64_22`
45×	`log-div_binary64_165` `associate-*r/_binary64_20`
44×	`+-commutative_binary64_8`
42×	`distribute-neg-frac_binary64_42`
31×	`exp-to-pow_binary64_140`
30×	`associate-*l/_binary64_21`
24×	`unpow3_binary64_144`
22×	`distribute-lft-neg-out_binary64_37`
21×	`unsub-neg_binary64_72`
20×	`distribute-neg-in_binary64_39`
19×	`distribute-rgt-neg-out_binary64_38`
17×	`div-sub_binary64_83` `distribute-rgt-out_binary64_31`
15×	`exp-lft-sqr_binary64_133`
14×	`exp-diff_binary64_126` `cube-prod_binary64_106` `swap-sqr_binary64_45`
13×	`log-pow_binary64_167` `pow-sqr_binary64_51`
11×	`/-rgt-identity_binary64_69` `*-rgt-identity_binary64_68`
10×	`unpow1/3_binary64_145` `cube-div_binary64_107` `distribute-rgt-out--_binary64_32`
9×	`associate-+l+_binary64_11`
8×	`unpow2_binary64_143` `unpow1/2_binary64_142` `unpow1_binary64_136` `rem-sqrt-square_binary64_91`
7×	`pow-plus_binary64_141` `distribute-lft-out_binary64_29` `associate--r+_binary64_14`
6×	`cube-unmult_binary64_115` `*-lft-identity_binary64_67` `remove-double-neg_binary64_66` `distribute-rgt1-in_binary64_34` `associate--l+_binary64_15`
5×	`associate-+l-_binary64_13` `associate-+r+_binary64_10`
4×	`cube-mult_binary64_108` `associate--l-_binary64_16`
3×	`distribute-lft-out--_binary64_30`
2×	`log-rec_binary64_166` `rem-square-sqrt_binary64_90` `mul-1-neg_binary64_70` `cancel-sign-sub_binary64_43` `associate-+r-_binary64_12`
1×	`1-exp_binary64_122` `rem-3cbrt-lft_binary64_103` `*-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` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `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` `difference-of-squares_binary64_47` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate--r-_binary64_17`

Counts

217 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	444	12162
1	769	10970
2	1815	10638
3	4820	10608
4	5016	10608

prune557.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	141	8	149

Error

0.8b

Counts

149 → 8

Compiler

Compiled 7915 to 5604 computations (29.2% saved)

regimes3.7s (15.5%)

Accuracy

Total 0.1b remaining (14.8%)

Threshold costs 0.1b (14.8%)

Compiler

Compiled 46506 to 39549 computations (15% saved)

bsearch4.0ms (0%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64_9`
9×	`+-commutative_binary64_8`
8×	`sub-neg_binary64_71`
7×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
3×	`distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35`
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-inv_binary64_44` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39` `distribute-lft-neg-out_binary64_37`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	101
1	49	101
2	67	101
3	80	101
4	89	101
5	92	101
6	91	101

end0.0ms (0%)

sample4.1s (17.5%)

Algorithm

1×

intervals

Results

814.0ms	8000×	body	128	valid
435.0ms	4673×	body	128	nan

Compiler

Compiled 2638 to 2242 computations (15% saved)

Details

analyze1.7s (7%)

sample61.0ms (0.3%)

simplify55.0ms (0.2%)

prune2.0ms (0%)

localize20.0ms (0.1%)

rewrite517.0ms (2.2%)

series2.2s (9.4%)

simplify262.0ms (1.1%)

prune352.0ms (1.5%)

localize22.0ms (0.1%)

rewrite583.0ms (2.5%)

series2.2s (9.4%)

simplify192.0ms (0.8%)

prune400.0ms (1.7%)

localize28.0ms (0.1%)

rewrite370.0ms (1.6%)

series1.9s (7.9%)

simplify156.0ms (0.7%)

prune280.0ms (1.2%)

localize22.0ms (0.1%)

rewrite857.0ms (3.6%)

series2.8s (11.8%)

simplify309.0ms (1.3%)

prune557.0ms (2.4%)

regimes3.7s (15.5%)

bsearch4.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample4.1s (17.5%)

Profiling