Details

analyze1.4s (28.9%)

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)

sample56.0ms (1.2%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
14.0ms	169×	body	128	nan

Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify122.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64_84`
452×	`associate-/r/_binary64_24`
428×	`associate-*l/_binary64_21`
410×	`associate-/l/_binary64_25`
292×	`associate-*r/_binary64_20`
253×	`associate-l_binary64_19`
192×	`associate-r_binary64_18`
183×	`associate-/l*_binary64_23`
144×	`unswap-sqr_binary64_46`
105×	`cancel-sign-sub-inv_binary64_44`
95×	`associate-/r*_binary64_22`
68×	`distribute-rgt-neg-in_binary64_36`
63×	`distribute-neg-frac_binary64_42`
61×	`distribute-lft-neg-in_binary64_35`
60×	`div-sub_binary64_83`
58×	`*-commutative_binary64_9`
46×	`distribute-rgt-in_binary64_28`
39×	`distribute-lft-in_binary64_27`
37×	`sub-neg_binary64_71`
34×	`sqr-pow_binary64_50`
28×	`distribute-lft-neg-out_binary64_37`
27×	`distribute-rgt-neg-out_binary64_38`
24×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
20×	`pow-sqr_binary64_51`
18×	`pow-plus_binary64_141`
15×	`distribute-frac-neg_binary64_41`
11×	`div0_binary64_59` `+-commutative_binary64_8`
9×	`unsub-neg_binary64_72` `distribute-neg-in_binary64_39`
7×	`cube-unmult_binary64_115`
5×	`mul0-rgt_binary64_61`
4×	`cube-prod_binary64_106` `mul0-lft_binary64_60` `associate-+l-_binary64_13`
3×	`*-rgt-identity_binary64_68` `sub0-neg_binary64_65` `+-rgt-identity_binary64_63` `difference-of-sqr-1_binary64_48` `associate-+r-_binary64_12`
2×	`unpow2_binary64_143` `unpow1_binary64_136` `count-2_binary64_26` `associate-+l+_binary64_11` `associate-+r+_binary64_10`
1×	`1-exp_binary64_122` `-lft-identity_binary64_67` `remove-double-neg_binary64_66` `--rgt-identity_binary64_64` `-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-neg-out_binary64_40` `associate--r+_binary64_14`
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` `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-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-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` `/-rgt-identity_binary64_69` `+-lft-identity_binary64_62` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-squares_binary64_47` `swap-sqr_binary64_45` `cancel-sign-sub_binary64_43` `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` `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	73	29
3	149	29
4	442	29
5	1485	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

10.9b

Counts

1 → 1

Compiler

Compiled 19 to 19 computations (0% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (/.f64 Om Omc) 2)
0.5b	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.6b	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
9.6b	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite438.0ms (9.2%)

Algorithm

1×	rewrite-expression-head

Error

10.8b

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` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `flip3--_binary64_82` `flip--_binary64_53` `asin-acos_binary64_258` `pow-pow_binary64_150` `pow-to-exp_binary64_147`

Counts

4 → 173

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)))))
17.0ms	(/.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)

series2.0s (41.8%)

Error

1.8b

Counts

4 → 69

Calls

4 calls:

885.0ms	(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
691.0ms	(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
114.0ms	(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
71.0ms	(pow.f64 (/.f64 Om Omc) 2)

Compiler

Compiled 9301 to 8010 computations (13.9% saved)

simplify757.0ms (16%)

Algorithm

1×	egg-herbie

Rules

386×	`cancel-sign-sub-inv_binary64_44`
233×	`unswap-sqr_binary64_46`
228×	`sub-neg_binary64_71`
166×	`associate-+r+_binary64_10`
164×	`associate-l_binary64_19` `associate-r_binary64_18`
159×	`+-commutative_binary64_8`
157×	`associate-*r/_binary64_20`
155×	`sqr-pow_binary64_50`
150×	`associate-/l_binary64_23` `-commutative_binary64_9`
134×	`times-frac_binary64_84`
133×	`associate-/r*_binary64_22`
118×	`associate-*l/_binary64_21`
115×	`associate-+l+_binary64_11`
83×	`neg-sub0_binary64_73`
81×	`div-sub_binary64_83`
78×	`neg-mul-1_binary64_74`
60×	`associate--l+_binary64_15` `associate--r+_binary64_14`
58×	`associate-/l/_binary64_25`
48×	`distribute-rgt-in_binary64_28`
43×	`distribute-lft-in_binary64_27`
40×	`pow-sqr_binary64_51`
34×	`pow-plus_binary64_141`
32×	`unsub-neg_binary64_72`
27×	`unpow2_binary64_143`
26×	`*-rgt-identity_binary64_68`
25×	`unpow1_binary64_136` `/-rgt-identity_binary64_69`
23×	`distribute-neg-in_binary64_39` `distribute-rgt-neg-in_binary64_36`
22×	`*-lft-identity_binary64_67`
18×	`associate-/r/_binary64_24`
17×	`cube-div_binary64_107` `cube-prod_binary64_106` `distribute-lft-neg-in_binary64_35`
16×	`log-prod_binary64_164` `distribute-rgt-out_binary64_31`
12×	`log-div_binary64_165` `exp-prod_binary64_130` `cube-unmult_binary64_115`
10×	`rem-sqrt-square_binary64_91` `mul-1-neg_binary64_70`
9×	`log-pow_binary64_167` `swap-sqr_binary64_45`
7×	`distribute-neg-frac_binary64_42`
6×	`unpow3_binary64_144` `pow-base-1_binary64_138`
5×	`distribute-lft-neg-out_binary64_37`
4×	`cube-mult_binary64_108`
3×	`rem-square-sqrt_binary64_90`
2×	`exp-sum_binary64_124` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `distribute-rgt1-in_binary64_34` `distribute-rgt-out--_binary64_32` `distribute-lft-out_binary64_29` `associate-+r-_binary64_12`
1×	`log-rec_binary64_166` `exp-diff_binary64_126` `1-exp_binary64_122` `exp-1-e_binary64_121` `remove-double-neg_binary64_66` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `difference-of-squares_binary64_47` `distribute-lft-out--_binary64_30` `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` `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` `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_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` `count-2_binary64_26` `associate--l-_binary64_16`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	521	13271
1	1184	11197
2	3809	11188

Details

analyze1.4s (28.9%)

sample56.0ms (1.2%)

simplify122.0ms (2.6%)

prune2.0ms (0%)

localize13.0ms (0.3%)

rewrite438.0ms (9.2%)

series2.0s (41.8%)

simplify757.0ms (16%)

end0.0ms (0%)

Profiling