Details

Time bar (total: 8.6s)

analyze2.0s (23.7%)

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 24 to 20 computations (16.7% saved)

sample2.7s (31.2%)

Alt Table
StatusErrorProgram
10.6b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
Results
1.7s8256×body128valid
914.0ms4985×body128invalid
Compiler

Compiled 117 to 97 computations (17.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (/.f64 t l) 2)
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.9b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
9.8b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))

series423.0ms (4.9%)

Counts
4 → 144
Calls

4 calls:

376.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
25.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
11.0ms
(pow.f64 (/.f64 Om Omc) 2)
9.0ms
(pow.f64 (/.f64 t l) 2)

rewrite96.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
603×prod-diff_binary64
183×add-sqr-sqrt_binary64
177×log1p-expm1-u_binary64
177×expm1-log1p-u_binary64
173×add-log-exp_binary64
Counts
4 → 137
Calls

4 calls:

91.0ms
(pow.f64 (/.f64 t l) 2)
91.0ms
(pow.f64 (/.f64 Om Omc) 2)
91.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
91.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01770
137566
2472866
3598666
000
100

prune393.0ms (4.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New2756281
Fresh000
Picked101
Done000
Total2766282
Error
1.0b
Counts
282 → 6
Alt Table
StatusErrorProgram
32.7b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
10.7b
(asin.f64 (pow.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)) 1/4) 2))
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))
47.2b
(asin.f64 (*.f64 -1 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
10.6b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
46.5b
(asin.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
Compiler

Compiled 13512 to 10471 computations (22.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2))))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(*.f64 (/.f64 t l) (sqrt.f64 2))
0.9b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))

series238.0ms (2.8%)

Counts
4 → 144
Calls

4 calls:

198.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2))))
18.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))
12.0ms
(*.f64 (/.f64 t l) (sqrt.f64 2))
9.0ms
(pow.f64 (/.f64 Om Omc) 2)

rewrite89.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
287×prod-diff_binary64
178×add-sqr-sqrt_binary64
170×log1p-expm1-u_binary64
170×expm1-log1p-u_binary64
168×add-log-exp_binary64
Counts
4 → 128
Calls

4 calls:

84.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2))))
84.0ms
(pow.f64 (/.f64 Om Omc) 2)
84.0ms
(*.f64 (/.f64 t l) (sqrt.f64 2))
84.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01770
136470
2444170
3505470
000
100

prune295.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2675272
Fresh145
Picked101
Done000
Total2699278
Error
0.9b
Counts
278 → 9
Alt Table
StatusErrorProgram
47.2b
(asin.f64 (*.f64 -1 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
47.2b
(asin.f64 (*.f64 -1 (*.f64 (/.f64 l (*.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
32.7b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
1.7b
(pow.f64 (sqrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))) 2)
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 (*.f64 t (sqrt.f64 2)) l))))
10.6b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
1.4b
(asin.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2))))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))))
46.5b
(asin.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2))))))
Compiler

Compiled 9636 to 7371 computations (23.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2)))))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(/.f64 l (sqrt.f64 2))
0.9b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2))))))

series246.0ms (2.9%)

Counts
4 → 120
Calls

4 calls:

202.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2)))))
24.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2))))))
10.0ms
(/.f64 l (sqrt.f64 2))
10.0ms
(pow.f64 (/.f64 Om Omc) 2)

rewrite91.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
320×prod-diff_binary64
182×add-sqr-sqrt_binary64
174×log1p-expm1-u_binary64
174×expm1-log1p-u_binary64
172×add-log-exp_binary64
Counts
4 → 136
Calls

4 calls:

86.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2)))))
86.0ms
(pow.f64 (/.f64 Om Omc) 2)
86.0ms
(/.f64 l (sqrt.f64 2))
86.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01767
137067
2466467
3536467
000
100

prune309.0ms (3.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2551256
Fresh178
Picked011
Done000
Total2569265
Error
0.9b
Counts
265 → 9
Alt Table
StatusErrorProgram
47.2b
(asin.f64 (*.f64 -1 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
47.2b
(asin.f64 (*.f64 -1 (*.f64 (/.f64 l (*.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
32.7b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
1.7b
(pow.f64 (sqrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))) 2)
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2))))))
10.6b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
1.4b
(asin.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2))))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))))
46.5b
(asin.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2))))))
Compiler

Compiled 9413 to 7422 computations (21.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2)))))
0.2b
(pow.f64 (/.f64 Om Omc) 2)
0.4b
(*.f64 l (pow.f64 2 -1/2))
0.9b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2))))))

series233.0ms (2.7%)

Counts
4 → 132
Calls

4 calls:

199.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2)))))
20.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2))))))
9.0ms
(pow.f64 (/.f64 Om Omc) 2)
4.0ms
(*.f64 l (pow.f64 2 -1/2))

rewrite90.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
314×prod-diff_binary64
191×add-sqr-sqrt_binary64
184×log1p-expm1-u_binary64
184×expm1-log1p-u_binary64
180×add-cbrt-cube_binary64
Counts
4 → 117
Calls

4 calls:

86.0ms
(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2)))))
86.0ms
(pow.f64 (/.f64 Om Omc) 2)
86.0ms
(*.f64 l (pow.f64 2 -1/2))
86.0ms
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01870
139267
2477067
3540367
000
100

prune335.0ms (3.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2481249
Fresh167
Picked011
Done011
Total2499258
Error
0.9b
Counts
258 → 9
Alt Table
StatusErrorProgram
32.7b
(+.f64 (fma.f64 (*.f64 (cbrt.f64 (/.f64 (PI.f64) 2)) (cbrt.f64 (/.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (PI.f64) 2)) (neg.f64 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1))) (fma.f64 (neg.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))) 1 (*.f64 (acos.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1)))) 1)))
2.4b
(*.f64 (cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (sqrt.f64 1/2))))))) (pow.f64 (cbrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (sqrt.f64 1/2))))))) 2))
1.7b
(pow.f64 (sqrt.f64 (asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))) 2)
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (*.f64 l (pow.f64 2 -1/2))))))
47.2b
(asin.f64 (*.f64 -1 (*.f64 (/.f64 l (*.f64 t (sqrt.f64 2))) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2)))))))
10.6b
(expm1.f64 (log1p.f64 (asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (fma.f64 2 (pow.f64 (/.f64 t l) 2) 1))))))
1.4b
(asin.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2))))) (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (sqrt.f64 (hypot.f64 1 (*.f64 (/.f64 t l) (sqrt.f64 2)))))))
46.5b
(asin.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 1/2) l) t) (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 Om 2) (pow.f64 Omc 2))))))
1.2b
(asin.f64 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (hypot.f64 1 (/.f64 t (/.f64 l (sqrt.f64 2))))))
Compiler

Compiled 9016 to 7123 computations (21% saved)

regimes773.0ms (9%)

Accuracy

Total 0.5b remaining (41.7%)

Threshold costs 0.5b (41.7%)

Counts
44 → 1
Compiler

Compiled 19906 to 16189 computations (18.7% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01831
12331
22731
32931
43031
52931

end206.0ms (2.4%)

Compiler

Compiled 349 to 283 computations (18.9% saved)

Profiling

Loading profile data...