Details

Time bar (total: 57.7s)

sample155.0ms

Algorithm
intervals
Results
54.0ms131×body160valid
44.0ms228×body80nan
27.0ms125×body80valid

simplify375.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
375.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize53.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.5b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.5b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
71×times-frac
58×*-un-lft-identity
51×add-cube-cbrt
19×sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
6×div-inv
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times asin-acos clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 sqrt-div div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 156
Calls
4 calls:
Slowest
27.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
25.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(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))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
180.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
132.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
29.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.5s

Counts
152 → 168
Calls
152 calls:
Slowest
647.0ms
(/ (* (* (- 1 (* (/ Om Omc) (/ Om Omc))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1)) (fma (* (/ t l) (/ t l)) 2 1)))
440.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
421.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
274.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
266.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.9b

localize31.0ms

Local error

Found 4 expressions with local error:

9.8b
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
2.8b
(log (exp (* (/ Om Omc) (/ Om Omc))))
0.5b
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))
0.5b
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
52×add-sqr-sqrt
43×times-frac
28×add-cube-cbrt
25×sqrt-prod
14×distribute-lft-out-- difference-of-squares
13×pow1
10×log-pow
7×associate-/l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod associate-/r*
2×rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv asin-acos exp-prod clear-num frac-2neg sqrt-pow1 flip3-- exp-to-pow pow1/2 sqrt-div div-sub div-exp rem-log-exp flip--
Counts
4 → 117
Calls
4 calls:
Slowest
26.0ms
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))
16.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
15.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
1.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1)))
100.0ms
(/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))
50.0ms
(log (exp (* (/ Om Omc) (/ Om Omc))))
17.0ms
(asin (sqrt (/ (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify21.3s

Counts
101 → 129
Calls
101 calls:
Slowest
553.0ms
(sqrt (/ (* (cbrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc)))))) (cbrt (- 1 (log (exp (* (/ Om Omc) (/ Om Omc))))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
541.0ms
(- (* 1 1) (* (log (exp (* (/ Om Omc) (/ Om Omc)))) (log (exp (* (/ Om Omc) (/ Om Omc))))))
443.0ms
(sqrt (/ (+ (sqrt 1) (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
430.0ms
(/ (- 1 (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (fma (* (/ t l) (/ t l)) 2 1))
411.0ms
(sqrt (/ (+ (sqrt 1) (sqrt (log (exp (* (/ Om Omc) (/ Om Omc)))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.9b

localize50.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.8b
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
0.5b
(asin (sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
7×sqrt-prod
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/2 sqrt-div
2×rem-sqrt-square
1×frac-times asin-acos pow-prod-down associate-*l/ associate-*r/
Counts
4 → 60
Calls
4 calls:
Slowest
66.0ms
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
191.0ms
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
109.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
91.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
13.0ms
(asin (sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))

simplify3.6s

Counts
28 → 72
Calls
28 calls:
Slowest
660.0ms
(* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
322.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
281.0ms
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))))
264.0ms
(* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
237.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 10.9b

localize87.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
9.8b
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt pow1 sqrt-prod
7×*-un-lft-identity add-cube-cbrt
5×sqrt-pow1
4×expm1-log1p-u add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-div
1×frac-times pow-prod-down associate-*l/ associate-*r/
Counts
4 → 65
Calls
4 calls:
Slowest
75.0ms
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

series408.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))))
92.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
77.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
75.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.0s

Counts
33 → 77
Calls
33 calls:
Slowest
333.0ms
(sqrt (* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))))
298.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))))
227.0ms
(* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))
181.0ms
(* (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))
175.0ms
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.9b

regimes484.0ms

Accuracy

0% (0.1b remaining)

Error of 10.1b against oracle of 10.1b and baseline of 10.1b

bsearch3.0ms

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.1s3835×body160valid
1.7s7880×body80nan
929.0ms4165×body80valid