Details

Time bar (total: 49.3s)

sample129.0ms

Algorithm
intervals
Results
47.0ms117×body160valid
36.0ms253×body80nan
20.0ms139×body80valid

simplify300.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
300.0ms
(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: 11.4b

localize50.0ms

Local error

Found 4 expressions with local error:

10.4b
(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))))
0.2b
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite63.0ms

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
25.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
23.0ms
(* (/ Om Omc) (/ Om Omc))
11.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
2.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1)))
82.0ms
(/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))
36.0ms
(* (/ Om Omc) (/ Om Omc))
17.0ms
(asin (sqrt (/ (- 1 (* (/ Om Omc) (/ Om Omc))) (fma (* (/ t l) (/ t l)) 2 1))))

simplify14.6s

Counts
152 → 168
Calls
152 calls:
Slowest
686.0ms
(/ (* (* (- 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)))
501.0ms
(- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3))
454.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
282.0ms
(/ (- 1 (/ Om Omc)) (fma (* (/ t l) (/ t l)) 2 1))
270.0ms
(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)))))

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.3b

localize32.0ms

Local error

Found 4 expressions with local error:

10.4b
(sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1))))
0.6b
(asin (sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1)))))
0.2b
(/ 1 (fma (* (/ t l) (/ t l)) 2 1))
0.2b
(* (/ Om Omc) (/ Om Omc))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
49×times-frac
40×*-un-lft-identity add-cube-cbrt
20×add-exp-log
18×add-cbrt-cube
15×pow1
13×swap-sqr associate-*r* associate-*l*
6×sqrt-div div-exp
5×cbrt-undiv div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×frac-times associate-/r* associate-*l/ associate-/l*
2×sqrt-pow1 flip3-- pow-prod-down associate-*r/ flip--
1×pow2 rec-exp asin-acos clear-num frac-2neg pow-plus pow1/2 1-exp pow-sqr un-div-inv *-commutative pow-prod-up sqrt-prod pow-flip inv-pow
Counts
4 → 135
Calls
4 calls:
Slowest
25.0ms
(* (/ Om Omc) (/ Om Omc))
12.0ms
(sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1))))
8.0ms
(/ 1 (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(asin (sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1)))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1))))
92.0ms
(/ 1 (fma (* (/ t l) (/ t l)) 2 1))
37.0ms
(* (/ Om Omc) (/ Om Omc))
14.0ms
(asin (sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1)))))

simplify9.4s

Counts
123 → 147
Calls
123 calls:
Slowest
690.0ms
(sqrt (* (- (pow 1 3) (pow (* (/ Om Omc) (/ Om Omc)) 3)) 1))
499.0ms
(* (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))) (/ (* (cbrt Om) (cbrt Om)) (* (cbrt Omc) (cbrt Omc))))
481.0ms
(sqrt (* (- 1 (* (/ Om Omc) (/ Om Omc))) 1))
349.0ms
(* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1)))
338.0ms
(* (- 1 (* (/ Om Omc) (/ Om Omc))) (/ 1 (fma (* (/ t l) (/ t l)) 2 1)))

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.3b

localize77.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
15.3b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
15.3b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
8.5b
(sqrt (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1
11×add-sqr-sqrt sqrt-pow1
10×*-un-lft-identity
9×cbrt-prod pow1/3 add-cube-cbrt pow-flip
7×sqrt-prod
5×times-frac
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus pow1/2 sqrt-div div-inv inv-pow
Counts
4 → 75
Calls
4 calls:
Slowest
9.0ms
(sqrt (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series846.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
214.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
206.0ms
(sqrt (/ 1 (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1)))))
206.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify5.5s

Counts
43 → 87
Calls
43 calls:
Slowest
575.0ms
(* (fma (* (/ t l) (/ t l)) 2 1) (fma (* (/ t l) (/ t l)) 2 1))
219.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
212.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
205.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
203.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 11.3b

localize103.0ms

Local error

Found 4 expressions with local error:

15.3b
(cbrt (* (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
15.3b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
15.3b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
15.3b
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×pow3 rem-cbrt-cube
Counts
4 → 55
Calls
4 calls:
Slowest
38.0ms
(cbrt (* (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (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))
1.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

series751.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(cbrt (* (* (cbrt (fma (* (/ t l) (/ t l)) 2 1)) (cbrt (fma (* (/ t l) (/ t l)) 2 1))) (cbrt (fma (* (/ t l) (/ t l)) 2 1))))
189.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
178.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))
178.0ms
(cbrt (fma (* (/ t l) (/ t l)) 2 1))

simplify3.0s

Counts
23 → 67
Calls
23 calls:
Slowest
257.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
256.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))
241.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
240.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ 1 l)))) (* 2 (log (/ 1 t))))))
240.0ms
(exp (* 1/3 (- (+ (log 2) (* 2 (log (/ -1 l)))) (* 2 (log (/ -1 t))))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 11.3b

regimes446.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.1s8013×body80nan
2.0s3779×body160valid
902.0ms4221×body80valid