Details

Time bar (total: 1.3m)

sample183.0ms

Algorithm
intervals
Results
55.0ms140×body80valid
55.0ms116×body160valid
45.0ms201×body80nan

simplify916.0ms

Calls
1 calls:
Slowest
915.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune83.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize59.0ms

Local error

Found 4 expressions with local error:

12.2b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.7b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac
13×sqrt-prod
9×pow1
8×add-cbrt-cube add-exp-log
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u div-inv add-log-exp
3×associate-/r* associate-/l*
2×rem-sqrt-square associate-/l/
1×pow2 frac-times cbrt-undiv asin-acos clear-num frac-2neg pow-plus flip3-- pow1/2 sqrt-div div-sub div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
4 calls:
Slowest
10.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
8.0ms
(* (/ Om Omc) (/ Om Omc))
5.0ms
(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))))

series257.0ms

Calls
4 calls:
Slowest
134.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
88.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
17.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify13.2s

Calls
71 calls:
Slowest
914.0ms
(/ (* (* (- 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)))
611.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
533.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
512.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
395.0ms
(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize228.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
10.6b
(sqrt (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×rem-sqrt-square pow1/2 sqrt-div div-inv
Calls
4 calls:
Slowest
16.0ms
(sqrt (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
3.0ms
(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

Calls
4 calls:
Slowest
353.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
272.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
243.0ms
(sqrt (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
220.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify8.0s

Calls
27 calls:
Slowest
857.0ms
(exp (* 1/3 (- (+ (* 2 (log (/ -1 t))) (log 1/2)) (* 2 (log (/ -1 l))))))
794.0ms
(exp (* 1/3 (- (+ (log 1/2) (* 2 (log (/ 1 t)))) (* 2 (log (/ 1 l))))))
737.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
623.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
591.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))

prune3.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.3b

localize108.0ms

Local error

Found 4 expressions with local error:

17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
17.9b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite15.0ms

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
Calls
4 calls:
Slowest
2.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(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

Calls
4 calls:
Slowest
452.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
276.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
186.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
165.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify5.2s

Calls
24 calls:
Slowest
745.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
616.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
471.0ms
(cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
381.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
347.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))

prune2.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.3b

localize32.0ms

Local error

Found 4 expressions with local error:

17.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
17.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
17.5b
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
12.2b
(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
15×cbrt-div
7×sqrt-div
5×frac-times associate-*l/
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*r/ div-inv
1×pow1/2 sqrt-prod
Calls
4 calls:
Slowest
32.0ms
(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
3.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series1.0s

Calls
4 calls:
Slowest
282.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
281.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
279.0ms
(cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
163.0ms
(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))

simplify20.9s

Calls
62 calls:
Slowest
1000.0ms
(sqrt (* (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))))
821.0ms
(cbrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
791.0ms
(cbrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
767.0ms
(sqrt (* (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))))
766.0ms
(cbrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

prune5.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 13.3b

regimes1.1s

Accuracy

0% (0.1b remaining)

Error of 10.4b against oracle of 10.3b and baseline of 10.4b

bsearch14.0ms

end1.0ms

sample11.0s

Algorithm
intervals
Results
3.5s3790×body160valid
3.0s7974×body80nan
2.7s4210×body80valid