Details

Time bar (total: 32.4s)

sample154.0ms

Algorithm
intervals
Results
61.0ms110×body320valid
43.0ms144×body160valid
32.0ms233×body80nan
0.0ms2×body80valid

simplify335.0ms

Calls
1 calls:
Slowest
334.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune30.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.9b

localize65.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (- (* g g) (* h h)))
31.9b
(sqrt (- (* g g) (* h h)))
9.4b
(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
9.3b
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-div
8×add-sqr-sqrt sqrt-prod
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u frac-times pow1 flip3-- add-cbrt-cube sqrt-div associate-*r/ add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp
2×cbrt-prod rem-sqrt-square flip3-+ pow1/2 pow1/3 associate-*l/ flip-+ difference-of-squares
Calls
4 calls:
Slowest
14.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.0ms
(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
3.0ms
(sqrt (- (* g g) (* h h)))
3.0ms
(sqrt (- (* g g) (* h h)))

series586.0ms

Calls
4 calls:
Slowest
277.0ms
(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
253.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.0ms
(sqrt (- (* g g) (* h h)))
24.0ms
(sqrt (- (* g g) (* h h)))

simplify6.5s

Calls
38 calls:
Slowest
806.0ms
(cbrt (* (/ 1 (* 2 a)) (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
465.0ms
(cbrt (* (/ 1 (* 2 a)) (+ (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
376.0ms
(cbrt (* 1 (+ (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
328.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
326.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 32.8b

localize22.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (- (* g g) (* h h)))
31.9b
(sqrt (- (* g g) (* h h)))
9.3b
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
3.2b
(- (* g g) (* h h))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×cbrt-div flip3-- flip--
4×expm1-log1p-u pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×difference-of-squares
2×frac-times rem-sqrt-square pow1/2 associate-*r/
1×cbrt-prod sub-neg fma-neg pow1/3 diff-log prod-diff associate-*l/
Calls
4 calls:
Slowest
8.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.0ms
(sqrt (- (* g g) (* h h)))
7.0ms
(sqrt (- (* g g) (* h h)))
3.0ms
(- (* g g) (* h h))

series376.0ms

Calls
4 calls:
Slowest
299.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
36.0ms
(sqrt (- (* g g) (* h h)))
24.0ms
(sqrt (- (* g g) (* h h)))
17.0ms
(- (* g g) (* h h))

simplify4.0s

Calls
37 calls:
Slowest
565.0ms
(cbrt (* (/ 1 (* 2 a)) (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
280.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))
279.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
276.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
270.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))

prune1.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.6b

localize20.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (- (* g g) (* h h)))
31.9b
(sqrt (- (* g g) (* h h)))
3.2b
(- (* g g) (* h h))
3.2b
(- (* g g) (* h h))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
2×rem-sqrt-square sub-neg pow1/2 fma-neg diff-log prod-diff
Calls
4 calls:
Slowest
6.0ms
(sqrt (- (* g g) (* h h)))
6.0ms
(sqrt (- (* g g) (* h h)))
3.0ms
(- (* g g) (* h h))
2.0ms
(- (* g g) (* h h))

series100.0ms

Calls
4 calls:
Slowest
39.0ms
(sqrt (- (* g g) (* h h)))
25.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(- (* g g) (* h h))
17.0ms
(- (* g g) (* h h))

simplify2.0s

Calls
36 calls:
Slowest
318.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
280.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
233.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
215.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
132.0ms
(sqrt (* (cbrt (- (* g g) (* h h))) (cbrt (- (* g g) (* h h)))))

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 32.6b

localize23.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (- (* g g) (* h h)))
31.9b
(sqrt (- (* g g) (* h h)))
9.3b
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
3.2b
(- (* g g) (* h h))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×cbrt-div flip3-- flip--
4×expm1-log1p-u pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×difference-of-squares
2×frac-times rem-sqrt-square pow1/2 associate-*r/
1×cbrt-prod sub-neg fma-neg pow1/3 diff-log prod-diff associate-*l/
Calls
4 calls:
Slowest
8.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
3.0ms
(sqrt (- (* g g) (* h h)))
3.0ms
(sqrt (- (* g g) (* h h)))
3.0ms
(- (* g g) (* h h))

series346.0ms

Calls
4 calls:
Slowest
266.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
32.0ms
(sqrt (- (* g g) (* h h)))
29.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(- (* g g) (* h h))

simplify3.7s

Calls
37 calls:
Slowest
439.0ms
(cbrt (* (/ 1 (* 2 a)) (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
276.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
269.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
246.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))
245.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune1.3s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 32.6b

regimes1.1s

Accuracy

0% (2.1b remaining)

Error of 31.6b against oracle of 29.5b and baseline of 31.6b

bsearch4.0ms

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.8s3709×body320valid
2.2s4152×body160valid
1.9s8072×body80nan
26.0ms139×body80valid