Details

Time bar (total: 59.9s)

sample152.0ms

Algorithm
intervals
Results
47.0ms253×body80nan
45.0ms118×body160valid
26.0ms138×body80valid

simplify397.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
396.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize37.0ms

Local error

Found 4 expressions with local error:

10.7b
(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
(* (/ Om Omc) (/ Om Omc))
0.2b
(* (/ t l) (/ t l))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
96×times-frac
72×*-un-lft-identity
69×add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
9×div-inv
8×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
6×difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×asin-acos sqrt-pow1 pow1/2 sqrt-div
Counts
4 → 185
Calls
4 calls:
Slowest
22.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(* (/ t l) (/ t l))
9.0ms
(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

Counts
4 → 12
Calls
4 calls:
Slowest
181.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
32.0ms
(* (/ Om Omc) (/ Om Omc))
28.0ms
(* (/ t l) (/ t l))
15.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify9.8s

Counts
185 → 197
Calls
185 calls:
Slowest
416.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
363.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
306.0ms
(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)))))
284.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
284.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))

prune3.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.2b

localize53.0ms

Local error

Found 4 expressions with local error:

10.5b
(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))))
0.3b
(* (/ Om Omc) (/ Om Omc))
0.2b
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

rewrite63.0ms

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
28.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
25.0ms
(* (/ Om Omc) (/ Om Omc))
3.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
2.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
88.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
52.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(asin (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

simplify23.9s

Counts
206 → 189
Calls
206 calls:
Slowest
474.0ms
(sqrt (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)))
416.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
353.0ms
(/ (* (* (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))))
290.0ms
(asin (sqrt (/ (- 1 (/ (pow Om 2) (pow Omc 2))) (fma (/ (pow t 2) (pow l 2)) 2 1))))
282.0ms
(/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

prune3.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize47.0ms

Local error

Found 4 expressions with local error:

10.5b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.5b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
7.1b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
7.1b
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
16×add-sqr-sqrt
10×pow1 *-un-lft-identity sqrt-pow1 add-cube-cbrt
6×rem-sqrt-square pow1/2
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 76
Calls
4 calls:
Slowest
3.0ms
(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)))

series624.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
238.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
190.0ms
(sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
101.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
95.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify4.3s

Counts
44 → 88
Calls
44 calls:
Slowest
227.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
218.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
214.0ms
(exp (* 1/4 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
176.0ms
(sqrt (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
164.0ms
(sqrt (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.4b

localize71.0ms

Local error

Found 4 expressions with local error:

16.2b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
16.2b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.7b
(sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1)))
0.5b
(asin (* (/ 1 (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×sqrt-prod
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 sqrt-pow1
1×asin-acos pow1/2
Counts
4 → 60
Calls
4 calls:
Slowest
3.0ms
(sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1)))
3.0ms
(asin (* (/ 1 (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (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))

series575.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
213.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
183.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
163.0ms
(sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1)))
15.0ms
(asin (* (/ 1 (fabs (cbrt (fma (* (/ t l) (/ t l)) 2 1)))) (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (cbrt (fma (* (/ t l) (/ t l)) 2 1))))))

simplify3.9s

Counts
28 → 72
Calls
28 calls:
Slowest
378.0ms
(asin (* (pow (/ 1 (fma (/ (pow t 2) (pow l 2)) 2 1)) 1/6) (* (sqrt (- 1 (/ (pow Om 2) (pow Omc 2)))) (/ 1 (fabs (pow (fma (/ (pow t 2) (pow l 2)) 2 1) 1/3))))))
347.0ms
(asin (* (pow (/ 1 (fma (/ (pow t 2) (pow l 2)) 2 1)) 1/6) (* (sqrt (- 1 (/ (pow Om 2) (pow Omc 2)))) (/ 1 (fabs (pow (fma (/ (pow t 2) (pow l 2)) 2 1) 1/3))))))
276.0ms
(asin (* (pow (/ 1 (fma (/ (pow t 2) (pow l 2)) 2 1)) 1/6) (* (sqrt (- 1 (/ (pow Om 2) (pow Omc 2)))) (/ 1 (fabs (pow (fma (/ (pow t 2) (pow l 2)) 2 1) 1/3))))))
238.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
228.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.4b

regimes572.0ms

Accuracy

97% (0.2b remaining)

Error of 5.7b against oracle of 5.6b and baseline of 10.6b

bsearch14.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.1s3851×body160valid
1.7s7907×body80nan
939.0ms4149×body80valid