Details

Time bar (total: 34.2s)

sample219.0ms

Algorithm
intervals
Results
101.0ms117×body320valid
56.0ms136×body160valid
39.0ms208×body80nan
0.0ms3×body80valid

simplify326.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
325.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize65.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
8.6b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
7.8b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×cbrt-prod
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
6×pow1 cbrt-div times-frac
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
2×frac-times rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 pow1/3 associate-*r/ flip-+ flip--
1×associate-*l/ div-inv distribute-lft-out--
Counts
4 → 77
Calls
4 calls:
Slowest
28.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
24.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
15.0ms
(sqrt (- (* g g) (* h h)))
10.0ms
(sqrt (- (* g g) (* h h)))

series860.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
430.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
300.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
68.0ms
(sqrt (- (* g g) (* h h)))
62.0ms
(sqrt (- (* g g) (* h h)))

simplify6.4s

Counts
45 → 89
Calls
45 calls:
Slowest
433.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
378.0ms
(- (+ (* 1/18 (* (cbrt 1/2) (* (exp (* 1/3 (- (log (/ 1 (sqrt -1))) (+ (* 5 (log h)) (log a))))) (pow g 2)))) (* (cbrt 1/2) (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))))) (* 1/3 (* (cbrt 1/2) (* g (exp (* 1/3 (- (log -1) (+ (* 2 (log h)) (log a)))))))))
376.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
340.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
307.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune1.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 29.7b

localize57.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
8.6b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
2.8b
(- (* g g) (* h h))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod
6×pow1 *-un-lft-identity add-cube-cbrt add-log-exp
5×cbrt-div
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip-- difference-of-squares
2×frac-times rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ flip-+
1×cbrt-prod sub-neg fma-neg pow1/3 diff-log prod-diff associate-*l/
Counts
4 → 73
Calls
4 calls:
Slowest
24.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
19.0ms
(sqrt (- (* g g) (* h h)))
19.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(- (* g g) (* h h))

series613.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
463.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
60.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(sqrt (- (* g g) (* h h)))
35.0ms
(- (* g g) (* h h))

simplify4.2s

Counts
39 → 85
Calls
39 calls:
Slowest
391.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
342.0ms
(cbrt (* (/ -1/2 a) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))
312.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))
296.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
282.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune1.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 28.6b

localize50.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
2.8b
(- (* g g) (* h h))
2.8b
(- (* g g) (* h h))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 74
Calls
4 calls:
Slowest
22.0ms
(sqrt (- (* g g) (* h h)))
15.0ms
(sqrt (- (* g g) (* h h)))
8.0ms
(- (* g g) (* h h))
8.0ms
(- (* g g) (* h h))

series228.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
69.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(- (* g g) (* h h))
55.0ms
(sqrt (- (* g g) (* h h)))
44.0ms
(- (* g g) (* h h))

simplify2.9s

Counts
38 → 86
Calls
38 calls:
Slowest
684.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
315.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
235.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
224.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
218.0ms
(/ (exp (* g g)) (exp (* h h)))

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.6b

localize46.0ms

Local error

Found 4 expressions with local error:

29.0b
(sqrt (- (* g g) (* h h)))
29.0b
(sqrt (- (* g g) (* h h)))
2.8b
(- (* g g) (* h h))
2.8b
(- (* g g) (* h h))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 74
Calls
4 calls:
Slowest
18.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(- (* g g) (* h h))
15.0ms
(sqrt (- (* g g) (* h h)))
8.0ms
(- (* g g) (* h h))

series206.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
66.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(sqrt (- (* g g) (* h h)))
42.0ms
(- (* g g) (* h h))
38.0ms
(- (* g g) (* h h))

simplify2.5s

Counts
38 → 86
Calls
38 calls:
Slowest
307.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
299.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
252.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
225.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
180.0ms
(/ (exp (* g g)) (exp (* h h)))

prune1.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.6b

regimes844.0ms

Accuracy

60.8% (1.5b remaining)

Error of 30.8b against oracle of 29.3b and baseline of 33.1b

bsearch379.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
2.8s4165×body160valid
2.7s3693×body320valid
1.6s7886×body80nan
26.0ms142×body80valid