Details

Time bar (total: 53.9s)

sample171.0ms

Algorithm
intervals
Results
53.0ms234×body80nan
49.0ms99×body160valid
37.0ms157×body80valid

simplify363.0ms

Calls
1 calls:
Slowest
362.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize47.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.6b
(asin (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))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite14.0ms

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
5.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
4.0ms
(* (/ Om Omc) (/ Om Omc))
3.0ms
(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))))

series292.0ms

Calls
4 calls:
Slowest
148.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
93.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
37.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify9.9s

Calls
71 calls:
Slowest
658.0ms
(/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
613.0ms
(/ (* (* (- 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)))
558.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
321.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
287.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.7b

localize13.0ms

Local error

Found 4 expressions with local error:

10.6b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
0.6b
(asin (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))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite28.0ms

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
11.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
9.0ms
(* (/ 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))))

series367.0ms

Calls
4 calls:
Slowest
190.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
112.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
48.0ms
(* (/ Om Omc) (/ Om Omc))
16.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify8.7s

Calls
71 calls:
Slowest
564.0ms
(/ (* (* (- 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)))
421.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
308.0ms
(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)))))
274.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))
261.0ms
(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.7b

localize20.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.6b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.4b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×add-sqr-sqrt times-frac
35×*-un-lft-identity add-cube-cbrt
9×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l*
4×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×sqrt-div associate-/l/
1×pow2 frac-times cbrt-undiv rem-sqrt-square asin-acos sqrt-undiv clear-num frac-2neg pow-plus flip3-- pow1/2 div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
4 calls:
Slowest
6.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
4.0ms
(* (/ Om Omc) (/ Om Omc))
1.0ms
(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))))

series305.0ms

Calls
4 calls:
Slowest
174.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
91.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
28.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify17.4s

Calls
119 calls:
Slowest
484.0ms
(sqrt (- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))))
427.0ms
(* (cbrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (cbrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))))
345.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
293.0ms
(/ (* (* (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))))
280.0ms
(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.3b

localize16.0ms

Local error

Found 4 expressions with local error:

11.2b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
11.2b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
10.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.8b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×rem-sqrt-square
4×expm1-log1p-u pow1 add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Calls
4 calls:
Slowest
1.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
1.0ms
(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))

series593.0ms

Calls
4 calls:
Slowest
211.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
193.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
98.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
91.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.3s

Calls
36 calls:
Slowest
206.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
178.0ms
(sqrt (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
176.0ms
(sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
164.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
159.0ms
(sqrt (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.3b

regimes619.0ms

Accuracy

98.9% (0.1b remaining)

Error of 5.5b against oracle of 5.5b and baseline of 10.3b

bsearch16.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.6s7695×body80nan
1.6s3717×body160valid
1.1s4283×body80valid