Details

Time bar (total: 33.9s)

sample144.0ms

Algorithm
intervals
Results
48.0ms117×body320valid
48.0ms136×body160valid
29.0ms208×body80nan
0.0ms3×body80valid

simplify387.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
386.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.3b

localize55.0ms

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 (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-div
8×add-sqr-sqrt sqrt-prod
6×pow1 *-un-lft-identity add-cube-cbrt
4×frac-times flip3-- add-cbrt-cube sqrt-div associate-*r/ add-exp-log insert-posit16 flip-- add-log-exp
2×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow1/3 associate-*l/ flip-+ difference-of-squares
Counts
4 → 64
Calls
4 calls:
Slowest
53.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
53.0ms
(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
21.0ms
(sqrt (- (* g g) (* h h)))
14.0ms
(sqrt (- (* g g) (* h h)))

series935.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
422.0ms
(cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
405.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
59.0ms
(sqrt (- (* g g) (* h h)))
48.0ms
(sqrt (- (* g g) (* h h)))

simplify5.8s

Counts
40 → 76
Calls
40 calls:
Slowest
547.0ms
(cbrt (* (/ 1 (* 2 a)) (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
441.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
393.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
283.0ms
(cbrt (* 1 (+ (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
272.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ -1 a))) (log (/ -1 g))))) (cbrt -1/2))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 29.7b

localize63.0ms

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))

rewrite74.0ms

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 flip3-- flip--
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×difference-of-squares
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×cbrt-prod sub-neg pow1/3 diff-log associate-*l/
Counts
4 → 63
Calls
4 calls:
Slowest
46.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
12.0ms
(sqrt (- (* g g) (* h h)))
7.0ms
(- (* g g) (* h h))
7.0ms
(sqrt (- (* g g) (* h h)))

series604.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
432.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
64.0ms
(sqrt (- (* g g) (* h h)))
61.0ms
(sqrt (- (* g g) (* h h)))
47.0ms
(- (* g g) (* h h))

simplify4.3s

Counts
37 → 75
Calls
37 calls:
Slowest
990.0ms
(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))))
273.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
242.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))
226.0ms
(cbrt (* 1 (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 28.3b

localize66.0ms

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))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt
4×flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 flip-- difference-of-squares
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 62
Calls
4 calls:
Slowest
14.0ms
(- (* g g) (* h h))
14.0ms
(sqrt (- (* g g) (* h h)))
14.0ms
(- (* g g) (* h h))
14.0ms
(sqrt (- (* g g) (* h h)))

series196.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
61.0ms
(sqrt (- (* g g) (* h h)))
53.0ms
(sqrt (- (* g g) (* h h)))
49.0ms
(- (* g g) (* h h))
33.0ms
(- (* g g) (* h h))

simplify2.1s

Counts
34 → 74
Calls
34 calls:
Slowest
243.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
240.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
234.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
234.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
196.0ms
(/ (exp (* g g)) (exp (* h h)))

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.3b

localize51.0ms

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))

rewrite55.0ms

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 flip3-- flip--
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×difference-of-squares
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×cbrt-prod sub-neg pow1/3 diff-log associate-*l/
Counts
4 → 63
Calls
4 calls:
Slowest
32.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.0ms
(- (* g g) (* h h))
7.0ms
(sqrt (- (* g g) (* h h)))
7.0ms
(sqrt (- (* g g) (* h h)))

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
398.0ms
(cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
78.0ms
(sqrt (- (* g g) (* h h)))
70.0ms
(sqrt (- (* g g) (* h h)))
45.0ms
(- (* g g) (* h h))

simplify4.0s

Counts
37 → 75
Calls
37 calls:
Slowest
591.0ms
(cbrt (* (/ 1 (* 2 a)) (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
371.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
291.0ms
(cbrt (* 1 (- (pow (- g) 3) (pow (sqrt (- (* g g) (* h h))) 3))))
267.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
255.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.3b

regimes1.2s

Accuracy

56.2% (1.9b remaining)

Error of 30.9b against oracle of 29.0b and baseline of 33.3b

bsearch320.0ms

end0.0ms

sample7.4s

Algorithm
intervals
Results
3.0s3693×body320valid
2.1s7886×body80nan
1.9s4165×body160valid
29.0ms142×body80valid