Details

Time bar (total: 28.9s)

sample186.0ms

Algorithm
intervals
Results
56.0ms118×body160valid
54.0ms242×body80nan
39.0ms138×body80valid

simplify1.3s

Counts
1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize41.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.3b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
Slowest
16.0ms
(* (/ Om Omc) (/ Om Omc))
14.0ms
(* (/ t l) (/ t l))
7.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
50.0ms
(* (/ Om Omc) (/ Om Omc))
27.0ms
(* (/ t l) (/ t l))
14.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.0s

Counts
197 → 197

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.9b

localize40.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
2.0b
(log (exp (* (/ Om Omc) (/ Om Omc))))
0.3b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×times-frac
56×*-un-lft-identity
44×add-cube-cbrt
25×sqrt-prod
16×pow1 add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
6×log-pow distribute-lft-out-- difference-of-squares
5×div-inv add-log-exp
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×log-prod
2×rem-sqrt-square
1×pow2 frac-times asin-acos exp-prod sqrt-pow1 pow-plus exp-to-pow pow1/2 sqrt-div rem-log-exp pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 138
Calls
4 calls:
Slowest
18.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
5.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
5.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
33.0ms
(* (/ Om Omc) (/ Om Omc))
28.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
11.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify1.5s

Counts
150 → 150

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.9b

localize59.0ms

Local error

Found 4 expressions with local error:

16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
11.5b
(sqrt (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
618×times-frac
500×sqrt-prod
351×add-sqr-sqrt
322×*-un-lft-identity
318×cbrt-prod
286×add-cube-cbrt
72×difference-of-squares
11×rem-sqrt-square
7×div-inv
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 382
Calls
4 calls:
Slowest
15.0ms
(sqrt (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
461.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
300.0ms
(sqrt (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
190.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
182.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.3s

Counts
394 → 394

prune7.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 10.9b

localize146.0ms

Local error

Found 4 expressions with local error:

16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.5b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series601.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
163.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
138.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
136.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify1.6s

Counts
68 → 68

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 10.9b

regimes589.0ms

Accuracy

0% (0.1b remaining)

Error of 10.3b against oracle of 10.2b and baseline of 10.3b

bsearch5.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
1.9s8039×body80nan
1.7s3808×body160valid
886.0ms4192×body80valid