Details

Time bar (total: 36.4s)

sample220.0ms

Algorithm
intervals
Results
96.0ms125×body320valid
48.0ms272×body80nan
48.0ms125×body160valid
1.0ms6×body80valid

simplify308.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
308.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.1b

localize44.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (- (* g g) (* h h)))
28.5b
(sqrt (- (* g g) (* h h)))
9.6b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
8.3b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))

rewrite102.0ms

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
36.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
29.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
18.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(sqrt (- (* g g) (* h h)))

series860.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
407.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
335.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
60.0ms
(sqrt (- (* g g) (* h h)))
58.0ms
(sqrt (- (* g g) (* h h)))

simplify6.2s

Counts
45 → 89
Calls
45 calls:
Slowest
445.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
355.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
351.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
349.0ms
(- (+ (* 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)))))))))
336.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune1.5s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.2b

localize39.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (- (* g g) (* h h)))
28.5b
(sqrt (- (* g g) (* h h)))
9.6b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
3.8b
(- (* g g) (* h h))

rewrite61.0ms

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
21.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
16.0ms
(- (* g g) (* h h))
14.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series597.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
411.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
84.0ms
(sqrt (- (* g g) (* h h)))
51.0ms
(- (* g g) (* h h))
51.0ms
(sqrt (- (* g g) (* h h)))

simplify4.0s

Counts
39 → 85
Calls
39 calls:
Slowest
374.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
369.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
294.0ms
(cbrt (* (/ -1/2 a) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))
281.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
254.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune1.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.4b

localize56.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (- (* g g) (* h h)))
28.5b
(sqrt (- (* g g) (* h h)))
9.6b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
3.8b
(- (* g g) (* h h))

rewrite63.0ms

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
21.0ms
(sqrt (- (* g g) (* h h)))
19.0ms
(sqrt (- (* g g) (* h h)))
14.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
8.0ms
(- (* g g) (* h h))

series631.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
433.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
75.0ms
(sqrt (- (* g g) (* h h)))
64.0ms
(sqrt (- (* g g) (* h h)))
59.0ms
(- (* g g) (* h h))

simplify4.5s

Counts
39 → 85
Calls
39 calls:
Slowest
685.0ms
(cbrt (* (/ -1/2 a) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))
343.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
328.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
328.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
270.0ms
(* (exp (* 1/3 (- (+ (log (sqrt -1)) (log h)) (log a)))) (cbrt -1/2))

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 28.4b

localize81.0ms

Local error

Found 4 expressions with local error:

28.5b
(sqrt (- (* g g) (* h h)))
28.5b
(sqrt (- (* g g) (* h h)))
28.5b
(sqrt (- (* g g) (* h h)))
28.5b
(sqrt (- (* g g) (* h h)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-prod
12×add-sqr-sqrt
8×pow1 *-un-lft-identity sqrt-div add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 flip3-- add-cbrt-cube pow1/2 add-exp-log insert-posit16 log1p-expm1-u flip-- add-log-exp difference-of-squares
Counts
4 → 76
Calls
4 calls:
Slowest
18.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(sqrt (- (* g g) (* h h)))
15.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
71.0ms
(sqrt (- (* g g) (* h h)))
66.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(sqrt (- (* g g) (* h h)))

simplify3.9s

Counts
44 → 88
Calls
44 calls:
Slowest
344.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
337.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
287.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
281.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
267.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune1.7s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 28.4b

regimes655.0ms

Accuracy

59% (1.5b remaining)

Error of 31.4b against oracle of 29.9b and baseline of 33.6b

bsearch131.0ms

end0.0ms

sample7.5s

Algorithm
intervals
Results
2.7s3703×body320valid
2.3s8017×body80nan
1.9s4140×body160valid
63.0ms157×body80valid