Details

Time bar (total: 2.6m)

sample155.0ms

Algorithm
intervals
Results
46.0ms115×body160valid
40.0ms195×body80nan
30.0ms141×body80valid

simplify383.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
382.0ms
(asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2))))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize25.0ms

Local error

Found 4 expressions with local error:

10.0b
(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))
0.3b
(* (/ t l) (/ t l))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
111×times-frac
86×*-un-lft-identity
79×add-cube-cbrt
30×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
19×pow1 sqrt-prod
14×difference-of-squares
10×div-inv
9×cbrt-undiv div-exp
8×prod-exp cbrt-unprod unswap-sqr
5×associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r*
2×pow2 frac-times rem-sqrt-square pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up associate-/l/
1×clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub flip--
Counts
4 → 215
Calls
4 calls:
Slowest
13.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
12.0ms
(* (/ t l) (/ t l))
12.0ms
(* (/ Om Omc) (/ Om Omc))
10.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
202.0ms
(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
(* (/ t l) (/ t l))
28.0ms
(* (/ Om Omc) (/ Om Omc))

simplify15.9s

Counts
227 → 227
Calls
227 calls:
Slowest
577.0ms
(/ (* (* (- 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)))
455.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
432.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
386.0ms
(* (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))) (/ (* (cbrt t) (cbrt t)) (* (cbrt l) (cbrt l))))
299.0ms
(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)))))

prune3.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.5b

localize47.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.0b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
0.3b
(* (/ t l) (/ t l))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
434×times-frac
411×sqrt-prod
272×add-sqr-sqrt
241×*-un-lft-identity
205×add-cube-cbrt
72×difference-of-squares
16×add-cbrt-cube add-exp-log
14×pow1
13×swap-sqr associate-*r* associate-*l*
11×div-inv
9×rem-sqrt-square
4×expm1-log1p-u cbrt-undiv div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2
1×pow2 frac-times pow-plus sqrt-div pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 330
Calls
4 calls:
Slowest
22.0ms
(* (/ t l) (/ t l))
9.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (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))

series342.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
76.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
73.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
26.0ms
(* (/ t l) (/ t l))

simplify46.1s

Counts
314 → 342
Calls
314 calls:
Slowest
728.0ms
(/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))
645.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
393.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))
392.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
391.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (sqrt (fma (* (/ t l) (/ t l)) 2 1)))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))))

prune6.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 10.5b

localize75.0ms

Local error

Found 4 expressions with local error:

10.3b
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
10.3b
(sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))
10.0b
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))))
0.5b
(cbrt l)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
411×sqrt-prod
394×times-frac
233×add-sqr-sqrt
214×*-un-lft-identity
178×add-cube-cbrt
72×difference-of-squares
9×rem-sqrt-square
7×pow1 div-inv
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod sqrt-pow1 pow1/2
1×pow1/3 sqrt-div
Counts
4 → 274
Calls
4 calls:
Slowest
10.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))))
1.0ms
(cbrt l)
1.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))

series774.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
309.0ms
(cbrt l)
250.0ms
(sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))))
132.0ms
(sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))
83.0ms
(sqrt (fma (* (/ t l) (/ t l)) 2 1))

simplify48.7s

Counts
242 → 286
Calls
242 calls:
Slowest
652.0ms
(sqrt (/ (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1)))))
648.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))
389.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))) (* (cbrt (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))) (cbrt (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1))))))
388.0ms
(sqrt (sqrt (/ (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1)))))
373.0ms
(sqrt (/ (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (* (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (sqrt (fma (* (/ t l) (/ t l)) 2 1))))) (sqrt (sqrt (fma (* (/ (/ t l) (cbrt l)) (/ (/ t (cbrt l)) (cbrt l))) 2 1)))))

prune6.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 10.5b

localize65.0ms

Local error

Found 4 expressions with local error:

10.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
10.0b
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
4.8b
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
4.8b
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
124×sqrt-prod
68×add-sqr-sqrt
64×times-frac
54×*-un-lft-identity
42×add-cube-cbrt
24×difference-of-squares
10×pow1 rem-sqrt-square sqrt-pow1
6×pow1/2 sqrt-div
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
4 → 148
Calls
4 calls:
Slowest
12.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
11.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
10.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

series811.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
250.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
231.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
189.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
141.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))

simplify17.6s

Counts
116 → 160
Calls
116 calls:
Slowest
314.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
301.0ms
(sqrt (sqrt (/ (* (cbrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (cbrt (- 1 (* (/ Om Omc) (/ Om Omc))))) (sqrt (fma (* (/ t l) (/ t l)) 2 1)))))
291.0ms
(sqrt (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))
285.0ms
(sqrt (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))))))
285.0ms
(sqrt (/ (sqrt (- 1 (* (/ Om Omc) (/ Om Omc)))) (sqrt (fma (* (/ t l) (/ t l)) 2 1))))

prune2.9s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 10.5b

regimes373.0ms

Accuracy

0% (0.1b remaining)

Error of 10.5b against oracle of 10.4b and baseline of 10.5b

bsearch3.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.1s3853×body160valid
2.0s7980×body80nan
932.0ms4147×body80valid