Details

Time bar (total: 15.1s)

analyze1.5s (9.6%)

Algorithm
1×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)

sample53.0ms (0.3%)

Algorithm
1×intervals
Results
23.0ms256×body128valid
11.0ms138×body128nan
Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify72.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
525×associate-/r/_binary64
484×unswap-sqr_binary64
458×associate-/l/_binary64
422×associate-*l/_binary64
301×*-commutative_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01729
13329
26129
315829
447629
5162329
6342929
7463129
8495029
9489829

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
9.7b
Counts
1 → 1
Alt Table
StatusErrorProgram
▶9.7b
(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 46 to 38 computations (17.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite440.0ms (2.9%)

Algorithm
1×rewrite-expression-head
Error
9.7b
Rules
143×add-sqr-sqrt_binary64
108×times-frac_binary64
98×*-un-lft-identity_binary64
70×difference-of-squares_binary64
49×add-cube-cbrt_binary64
Counts
4 → 173
Calls

4 calls:

22.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
18.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
5.0ms
(pow.f64 (/.f64 t l) 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 5892 to 4086 computations (30.7% saved)

series449.0ms (3%)

Error
1.7b
Counts
4 → 58
Calls

4 calls:

186.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
170.0ms
(/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
46.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
21.0ms
(pow.f64 (/.f64 t l) 2)
Compiler

Compiled 4757 to 3971 computations (16.5% saved)

simplify316.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
754×associate-/l*_binary64
253×associate-/r/_binary64
202×associate-/l/_binary64
162×distribute-rgt-in_binary64
141×distribute-lft-in_binary64
Counts
231 → 169
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03409446
17218112
219707967
347787967
449947967
549567967

prune129.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1645169
Fresh000
Picked011
Done000
Total1646170
Error
0.7b
Counts
170 → 6
Alt Table
StatusErrorProgram
45.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
✓9.7b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
42.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
▶9.9b
(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))))))))
14.1b
(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))
40.4b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (*.f64 t (pow.f64 (/.f64 (sqrt.f64 t) l) 2)))))))
Compiler

Compiled 2493 to 1689 computations (32.3% 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))))))
15.9b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.9b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite441.0ms (2.9%)

Algorithm
1×rewrite-expression-head
Error
0.7b
Rules
145×cbrt-prod_binary64
140×add-sqr-sqrt_binary64
118×times-frac_binary64
108×sqrt-prod_binary64
95×*-un-lft-identity_binary64
Counts
4 → 157
Calls

4 calls:

25.0ms
(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 9590 to 6953 computations (27.5% saved)

series656.0ms (4.4%)

Error
0.7b
Counts
4 → 57
Calls

4 calls:

368.0ms
(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))))))
90.0ms
(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))))))))
66.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
64.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
Compiler

Compiled 9544 to 7855 computations (17.7% saved)

simplify246.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
601×associate-*l/_binary64
241×associate-/r/_binary64
180×cancel-sign-sub-inv_binary64
143×unswap-sqr_binary64
136×associate-/l/_binary64
Counts
214 → 150
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042511964
181110552
222809881
350499881

prune161.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1491150
Fresh044
Picked011
Done011
Total1497156
Error
0.7b
Counts
156 → 7
Alt Table
StatusErrorProgram
▶11.0b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (pow.f64 (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))) (cbrt.f64 (asin.f64 (pow.f64 (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)))) (cbrt.f64 (asin.f64 (pow.f64 (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))))
45.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
✓9.7b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
42.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
✓9.9b
(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))))))))
14.1b
(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))
40.4b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (*.f64 t (pow.f64 (/.f64 (sqrt.f64 t) l) 2)))))))
Compiler

Compiled 4378 to 3136 computations (28.4% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.3b
(cbrt.f64 (asin.f64 (pow.f64 (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)))
15.9b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.9b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
15.9b
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))

rewrite182.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Error
0.7b
Rules
12×cbrt-prod_binary64
8×*-un-lft-identity_binary64
8×add-sqr-sqrt_binary64
8×add-cube-cbrt_binary64
6×cbrt-div_binary64
Counts
4 → 50
Calls

4 calls:

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))))
1.0ms
(cbrt.f64 (asin.f64 (pow.f64 (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)))
Compiler

Compiled 4424 to 3361 computations (24% saved)

series551.0ms (3.7%)

Error
0.7b
Counts
4 → 48
Calls

4 calls:

229.0ms
(cbrt.f64 (asin.f64 (pow.f64 (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)))
85.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
83.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
81.0ms
(cbrt.f64 (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))
Compiler

Compiled 9229 to 7506 computations (18.7% saved)

simplify137.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
325×associate-/r/_binary64
274×associate-/l/_binary64
269×unswap-sqr_binary64
258×associate-*l*_binary64
236×associate-*r*_binary64
Counts
98 → 53
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01102978
12602780
26052717
322842480
449522480
549272480

prune92.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New52153
Fresh044
Picked101
Done022
Total53760
Error
0.7b
Counts
60 → 7
Alt Table
StatusErrorProgram
26.2b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (cbrt.f64 (-.f64 1 (*.f64 4 (pow.f64 (/.f64 t l) 4)))) (cbrt.f64 (-.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))) 3))) (cbrt.f64 (asin.f64 (pow.f64 (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)))) (cbrt.f64 (asin.f64 (pow.f64 (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))))
45.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
✓9.7b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
42.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
✓9.9b
(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))))))))
▶14.1b
(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))
40.4b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (*.f64 t (pow.f64 (/.f64 (sqrt.f64 t) l) 2)))))))
Compiler

Compiled 2628 to 1988 computations (24.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b
(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)
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))))))
8.3b
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
13.5b
(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))

rewrite227.0ms (1.5%)

Algorithm
1×rewrite-expression-head
Error
0.7b
Rules
70×add-sqr-sqrt_binary64
49×times-frac_binary64
49×*-un-lft-identity_binary64
48×sqrt-prod_binary64
30×difference-of-squares_binary64
Counts
4 → 112
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)))))
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))
2.0ms
(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
(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 4079 to 2978 computations (27% saved)

series430.0ms (2.9%)

Error
0.7b
Counts
4 → 55
Calls

4 calls:

188.0ms
(sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2)))))
128.0ms
(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)
50.0ms
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
46.0ms
(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 4656 to 3958 computations (15% saved)

simplify251.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
541×associate-/r*_binary64
537×associate-/l*_binary64
356×associate-*l/_binary64
244×unswap-sqr_binary64
146×log-prod_binary64
Counts
167 → 134
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02707691
15276523
214046382
346896382
449796382
549696382

prune80.0ms (0.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1322134
Fresh134
Picked011
Done022
Total1338141
Error
0.7b
Counts
141 → 8
Alt Table
StatusErrorProgram
26.2b
(*.f64 (*.f64 (cbrt.f64 (asin.f64 (pow.f64 (sqrt.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (cbrt.f64 (-.f64 1 (*.f64 4 (pow.f64 (/.f64 t l) 4)))) (cbrt.f64 (-.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))) 3))) (cbrt.f64 (asin.f64 (pow.f64 (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)))) (cbrt.f64 (asin.f64 (pow.f64 (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))))
45.0b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (neg.f64 (/.f64 (*.f64 l (sqrt.f64 1/2)) t))))
10.4b
(*.f64 (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)))))) 2)) (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))))))))
13.7b
(cbrt.f64 (pow.f64 (*.f64 (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)))))) 2)) (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)))))))) 3))
9.7b
(asin.f64 (sqrt.f64 (/.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2)) (+.f64 1 (*.f64 2 (pow.f64 (/.f64 t l) 2))))))
42.6b
(asin.f64 (*.f64 (sqrt.f64 (-.f64 1 (pow.f64 (/.f64 Om Omc) 2))) (/.f64 (*.f64 l (sqrt.f64 1/2)) t)))
9.9b
(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))))))))
14.1b
(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 1694 to 1237 computations (27% saved)

regimes6.5s (43.3%)

Accuracy

Total 0.1b remaining (9.7%)

Threshold costs 0.1b (9.7%)

Compiler

Compiled 141736 to 111930 computations (21% saved)

bsearch9.0ms (0.1%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify7.0ms (0%)

Algorithm
1×egg-herbie
Rules
11×*-commutative_binary64
9×+-commutative_binary64
8×sub-neg_binary64
7×neg-sub0_binary64
7×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03499
14999
26799
38099
48999
59299
69199

end2.0ms (0%)

Compiler

Compiled 68 to 48 computations (29.4% saved)

sample2.1s (13.7%)

Algorithm
1×intervals
Results
754.0ms8000×body128valid
418.0ms4764×body128nan
Compiler

Compiled 418 to 329 computations (21.3% saved)

Profiling

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