Details

Time bar (total: 52.5s)

sample151.0ms

Algorithm
intervals
Results
45.0ms270×body80nan
44.0ms117×body160valid
41.0ms139×body80valid

simplify260.0ms

Calls
1 calls:
Slowest
259.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.2b

localize40.0ms

Local error

Found 4 expressions with local error:

9.2b
(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))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite15.0ms

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
6.0ms
(/ (- 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))))

series330.0ms

Calls
4 calls:
Slowest
167.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
110.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
42.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify8.3s

Calls
71 calls:
Slowest
538.0ms
(/ (* (* (- 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)))
364.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
271.0ms
(sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
269.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
267.0ms
(/ (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.1b

localize9.0ms

Local error

Found 4 expressions with local error:

9.2b
(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))))
0.3b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite21.0ms

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
8.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
6.0ms
(* (/ Om Omc) (/ Om Omc))
4.0ms
(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))))

series285.0ms

Calls
4 calls:
Slowest
147.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
102.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
26.0ms
(* (/ Om Omc) (/ Om Omc))
10.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify7.7s

Calls
71 calls:
Slowest
579.0ms
(/ (* (* (- 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)))
499.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))
425.0ms
(- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc))))
235.0ms
(- (log (- 1 (* (/ Om Omc) (/ Om Omc)))) (log (fma (* (/ t l) (/ t l)) 2 1)))
213.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.1b

localize21.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
0.7b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
0.5b
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite17.0ms

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
8.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
4.0ms
(* (/ Om Omc) (/ Om Omc))
2.0ms
(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))))

series306.0ms

Calls
4 calls:
Slowest
157.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
92.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
45.0ms
(* (/ Om Omc) (/ Om Omc))
13.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify17.9s

Calls
119 calls:
Slowest
437.0ms
(sqrt (- (* 1 1) (* (* (/ Om Omc) (/ Om Omc)) (* (/ Om Omc) (/ Om Omc)))))
406.0ms
(/ (* (* (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))))
313.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
287.0ms
(/ (cbrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
286.0ms
(/ (sqrt (sqrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize29.0ms

Local error

Found 4 expressions with local error:

8.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
8.9b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
7.4b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
7.4b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

rewrite14.0ms

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
8.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

series557.0ms

Calls
4 calls:
Slowest
190.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
188.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
91.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
87.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.4s

Calls
36 calls:
Slowest
214.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
200.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
182.0ms
(sqrt (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
176.0ms
(sqrt (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
168.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes714.0ms

Accuracy

98.6% (0.1b remaining)

Error of 6.0b against oracle of 6.0b and baseline of 10.6b

bsearch13.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.3s3746×body160valid
2.1s7815×body80nan
858.0ms4254×body80valid