Details

Time bar (total: 1.2m)

sample163.0ms

Algorithm
intervals
Results
73.0ms131×body160valid
39.0ms200×body80nan
25.0ms125×body80valid

simplify353.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
352.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize47.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.4b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.4b
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(* (/ t l) (/ t l))

rewrite49.0ms

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
26.0ms
(* (/ t l) (/ t l))
13.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
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))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
115.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
35.0ms
(* (/ t l) (/ t l))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.7s

Counts
152 → 168
Calls
152 calls:
Slowest
637.0ms
(/ (* (* (- 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)))
472.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
444.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
284.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))
275.0ms
(sqrt (/ (* (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)))))

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.4b

localize39.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.7b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.4b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(* (/ t l) (/ t l))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
85×add-sqr-sqrt
72×*-un-lft-identity
65×add-cube-cbrt sqrt-prod
18×add-cbrt-cube add-exp-log
14×difference-of-squares
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×associate-/l*
6×associate-/r*
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
2×sqrt-div associate-/l/
1×pow2 frac-times rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg sqrt-pow1 pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 177
Calls
4 calls:
Slowest
12.0ms
(* (/ t l) (/ t l))
10.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
6.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
100.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
39.0ms
(* (/ t l) (/ t l))
16.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify23.7s

Counts
206 → 189
Calls
206 calls:
Slowest
463.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
443.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
363.0ms
(/ (* (* (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (* (sqrt (fma (* (/ t l) (/ t l)) 2 1)) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
296.0ms
(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
285.0ms
(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize77.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1)))
0.6b
(cbrt l)
0.6b
(cbrt l)
0.6b
(cbrt l)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity sqrt-prod
16×times-frac add-cube-cbrt
9×cbrt-prod
6×difference-of-squares
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 76
Calls
4 calls:
Slowest
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1)))
1.0ms
(cbrt l)
1.0ms
(cbrt l)
1.0ms
(cbrt l)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
324.0ms
(cbrt l)
282.0ms
(cbrt l)
257.0ms
(cbrt l)
247.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1)))

simplify7.4s

Counts
44 → 88
Calls
44 calls:
Slowest
648.0ms
(sqrt (/ 1 (sqrt (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1))))
491.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1)))))
486.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1))
459.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1))))
458.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1)) (cbrt (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (cbrt l))) 2 1)))))

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

localize98.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))))) 2 1)))
0.6b
(cbrt (cbrt l))
0.6b
(cbrt (cbrt l))
0.6b
(cbrt (cbrt l))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
25×add-sqr-sqrt
22×*-un-lft-identity
19×add-cube-cbrt sqrt-prod
16×times-frac
6×difference-of-squares
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 sqrt-div div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
5.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))))) 2 1)))
1.0ms
(cbrt (cbrt l))
1.0ms
(cbrt (cbrt l))
1.0ms
(cbrt (cbrt l))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
416.0ms
(cbrt (cbrt l))
403.0ms
(cbrt (cbrt l))
383.0ms
(cbrt (cbrt l))
172.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))))) 2 1)))

simplify5.4s

Counts
53 → 97
Calls
53 calls:
Slowest
727.0ms
(* (pow (cbrt -1) 1/3) (pow (* l -1) 1/9))
672.0ms
(* (pow (cbrt -1) 1/3) (pow (* l -1) 1/9))
664.0ms
(* (pow (cbrt -1) 1/3) (pow (* l -1) 1/9))
234.0ms
(sqrt (* (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))))) 2 1))) (cbrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))))) 2 1)))))
198.0ms
(sqrt (/ (+ 1 (/ Om Omc)) (sqrt (fma (* (* (/ t l) (/ 1 (* (cbrt l) (cbrt l)))) (/ t (* (* (cbrt (cbrt l)) (cbrt (cbrt l))) (cbrt (cbrt l))))) 2 1))))

prune1.8s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.2b

regimes629.0ms

Accuracy

97.7% (0.1b remaining)

Error of 5.9b against oracle of 5.8b and baseline of 10.6b

bsearch12.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.9s7944×body80nan
1.6s3820×body160valid
951.0ms4180×body80valid