Details

Time bar (total: 15.1s)

analyze1.4s (9%)

Algorithm
search
Search
TrueOtherFalseIter
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)

sample54.0ms (0.4%)

Algorithm
intervals
Results
23.0ms256×body128valid
13.0ms164×body128nan
Compiler

Compiled 39 to 43 computations (-10.3% saved)

simplify143.0ms (1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0489529
1489529

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
9.2b
Counts
2 → 1
Compiler

Compiled 38 to 38 computations (0% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.2b
(pow.f64 (/.f64 t l) 2)
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.3b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.5b
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.3b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

rewrite67.0ms (0.4%)

Algorithm
rewrite-expression-head
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
add-exp-log_binary64_116
distribute-lft-out--_binary64_30
add-cbrt-cube_binary64_114 pow1_binary64_139
add-log-exp_binary64_117 associate-/r/_binary64_24
div-inv_binary64_75 associate-/r*_binary64_22 pow-unpow_binary64_155
pow-exp_binary64_146 div-exp_binary64_129 flip-+_binary64_52 rem-sqrt-square_binary64_91 associate-/l/_binary64_25 flip3-+_binary64_81
pow-to-exp_binary64_147 sqrt-pow1_binary64_96 cbrt-undiv_binary64_112 flip3--_binary64_82 frac-2neg_binary64_89 pow-pow_binary64_150 flip--_binary64_53 sqrt-div_binary64_95 clear-num_binary64_77 asin-acos_binary64_258 div-sub_binary64_83 pow1/2_binary64_158
Counts
4 → 173
Calls

8 calls:

21.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
18.0ms
(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))))))
0.0ms
(*.f64 2 (pow.f64 (/.f64 t l) 2))

series1.4s (9.5%)

Counts
4 → 58
Calls

4 calls:

652.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
595.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
112.0ms
(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 3883 to 3583 computations (7.7% saved)

simplify115.0ms (0.8%)

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049868023
149868023

prune547.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2229231
Fresh000
Picked101
Done000
Total2239232
Error
0.5b
Counts
232 → 9
Compiler

Compiled 6945 to 4737 computations (31.8% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.2b
(pow.f64 (/.f64 t l) 2)
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.3b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
0.3b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
8.7b
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite57.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
155×sqrt-prod_binary64_94 add-sqr-sqrt_binary64_100
125×times-frac_binary64_84
112×*-un-lft-identity_binary64_78
70×difference-of-squares_binary64_47
63×add-cube-cbrt_binary64_113
41×unpow-prod-down_binary64_157
17×associate-/l*_binary64_23
15×unpow2_binary64_143 sqr-pow_binary64_50
add-exp-log_binary64_116
distribute-lft-out--_binary64_30
add-cbrt-cube_binary64_114 associate-/r*_binary64_22 sqrt-div_binary64_95 pow1_binary64_139
add-log-exp_binary64_117
pow-unpow_binary64_155
pow-exp_binary64_146 div-exp_binary64_129 flip-+_binary64_52 div-inv_binary64_75 associate-/r/_binary64_24 associate-/l/_binary64_25 flip3-+_binary64_81
pow-to-exp_binary64_147 sqrt-pow1_binary64_96 cbrt-undiv_binary64_112 rem-sqrt-square_binary64_91 flip3--_binary64_82 frac-2neg_binary64_89 pow-pow_binary64_150 flip--_binary64_53 sqrt-undiv_binary64_99 clear-num_binary64_77 asin-acos_binary64_258 pow1/2_binary64_158
Counts
4 → 194
Calls

8 calls:

21.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
5.0ms
(pow.f64 (/.f64 Om Omc) 2)
4.0ms
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
1.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.0ms
(*.f64 2 (pow.f64 (/.f64 t l) 2))

series936.0ms (6.2%)

Counts
4 → 52
Calls

4 calls:

584.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
162.0ms
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
117.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
72.0ms
(pow.f64 (/.f64 Om Omc) 2)
Compiler

Compiled 3364 to 3106 computations (7.7% saved)

simplify103.0ms (0.7%)

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
053199170

prune538.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2424246
Fresh178
Picked101
Done000
Total24411255
Error
0.4b
Counts
255 → 11
Compiler

Compiled 7918 to 5555 computations (29.8% saved)

localize18.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.1b
(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
7.4b
(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
7.4b
(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
8.7b
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
8.7b
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod_binary64_94
16×add-sqr-sqrt_binary64_100
12×sqrt-div_binary64_95
10×sqrt-pow1_binary64_96 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78 pow1_binary64_139
rem-sqrt-square_binary64_91 pow1/2_binary64_158
add-cbrt-cube_binary64_114 add-log-exp_binary64_117 flip-+_binary64_52 add-exp-log_binary64_116 flip3-+_binary64_81
Counts
4 → 72
Calls

8 calls:

5.0ms
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
4.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
4.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
3.0ms
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.0ms
(*.f64 2 (pow.f64 (/.f64 t l) 2))

series730.0ms (4.8%)

Counts
4 → 54
Calls

4 calls:

202.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
193.0ms
(sqrt.f64 (sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
171.0ms
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
163.0ms
(sqrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
Compiler

Compiled 3462 to 3156 computations (8.8% saved)

simplify116.0ms (0.8%)

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (90.0ms)

IterNodesCost
049912348
149912348

prune287.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1260126
Fresh01010
Picked011
Done000
Total12611137
Error
0.4b
Counts
137 → 11
Compiler

Compiled 5048 to 3732 computations (26.1% saved)

localize26.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
0.0b
(*.f64 2 (pow.f64 (/.f64 t l) 2))
8.3b
(sqrt.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
14.0b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
14.0b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite50.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64_109
add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78 pow1_binary64_139
cbrt-div_binary64_110
add-cbrt-cube_binary64_114 add-log-exp_binary64_117 add-exp-log_binary64_116
flip-+_binary64_52 pow1/3_binary64_160 sqrt-div_binary64_95 flip3-+_binary64_81
sqrt-pow1_binary64_96
sqrt-prod_binary64_94 frac-times_binary64_88 associate-*l/_binary64_21 pow-prod-down_binary64_149 associate-*r/_binary64_20 pow1/2_binary64_158
Counts
4 → 53
Calls

8 calls:

33.0ms
(sqrt.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.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))))
3.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
0.0ms
(*.f64 2 (pow.f64 (/.f64 t l) 2))

series1.2s (8.2%)

Counts
4 → 55
Calls

4 calls:

619.0ms
(sqrt.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))) (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))))
207.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
205.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
203.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
Compiler

Compiled 5218 to 4609 computations (11.7% saved)

simplify51.0ms (0.3%)

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
049752781
149752781

prune236.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1080108
Fresh099
Picked011
Done011
Total10811119
Error
0.4b
Counts
119 → 11
Compiler

Compiled 4747 to 3432 computations (27.7% saved)

simplify28.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
03451984
13451984

regimes1.8s (11.9%)

Compiler

Compiled 24588 to 22273 computations (9.4% saved)

bsearch99.0ms (0.7%)

Steps
ItersRangePoint
9
3.8058030968167636e+55
1.6577195150961209e+62
4.0699161400542827e+55
8
-1.4583992802605929e+75
-9.393181850110778e+71
-1.4397610098885724e+75
Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes526.0ms (3.5%)

Compiler

Compiled 3937 to 4247 computations (-7.9% saved)

bsearch79.0ms (0.5%)

Steps
ItersRangePoint
9
1.861661564049545e+62
1.2038330637544195e+69
2.7098674073710237e+62
6
-3.570121003959573e+142
-5.4156818031839816e+141
-3.5189165217235146e+142
Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes286.0ms (1.9%)

Compiler

Compiled 1805 to 2049 computations (-13.5% saved)

bsearch103.0ms (0.7%)

Steps
ItersRangePoint
9
1.861661564049545e+62
1.2038330637544195e+69
3.945702929768114e+68
11
-3.333898289371831e+129
-1.779361900494863e+109
-2.4191898762670895e+119
Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes261.0ms (1.7%)

Compiler

Compiled 1584 to 1828 computations (-15.4% saved)

bsearch44.0ms (0.3%)

Steps
ItersRangePoint
9
1.861661564049545e+62
1.2038330637544195e+69
4.0408429634684533e+68
Compiler

Compiled 3 to 5 computations (-66.7% saved)

regimes168.0ms (1.1%)

Compiler

Compiled 919 to 1121 computations (-22% saved)

bsearch0.0ms (0%)

regimes115.0ms (0.8%)

Compiler

Compiled 361 to 589 computations (-63.2% saved)

bsearch0.0ms (0%)

regimes92.0ms (0.6%)

Compiler

Compiled 122 to 256 computations (-109.8% saved)

bsearch89.0ms (0.6%)

Steps
ItersRangePoint
10
6.373917739296421e+136
6.99651677777606e+155
9.812738210921705e+151
7
-1.4677656003559478e+176
-3.8577324858497407e+174
-3.8979961988787077e+174
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes62.0ms (0.4%)

Accuracy

Total 0.1b remaining (14.5%)

Threshold costs 0.1b (14.5%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch95.0ms (0.6%)

Steps
ItersRangePoint
8
3.241569749400095e+112
8.916863151460572e+116
3.2969184450764058e+112
9
-5.985143844838235e+40
-5.880893675797835e+31
-4.132669693900505e+38
Compiler

Compiled 315 to 248 computations (21.3% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0220480
1220480

end0.0ms (0%)

sample3.1s (20.4%)

Algorithm
intervals
Results
736.0ms8000×body128valid
410.0ms4696×body128nan
Compiler

Compiled 1610 to 1416 computations (12% saved)

Pareto

0.3149642028529515

Profiling

Loading profile data...