Details

Time bar (total: 37.5s)

sample168.0ms

Algorithm
intervals
Results
63.0ms122×body320valid
49.0ms129×body160valid
36.0ms238×body80nan
1.0ms5×body80valid

simplify688.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
688.0ms
(+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h)))))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize40.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (- (* g g) (* h h)))
27.6b
(sqrt (- (* g g) (* h h)))
9.0b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
8.1b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))

rewrite53.0ms

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
20.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
13.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
10.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series836.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
364.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
342.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
67.0ms
(sqrt (- (* g g) (* h h)))
62.0ms
(sqrt (- (* g g) (* h h)))

simplify6.1s

Counts
45 → 89
Calls
45 calls:
Slowest
406.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
373.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
359.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
327.0ms
(- (+ (* 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)))))))))
312.0ms
(cbrt (* (/ -1/2 a) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))

prune1.4s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 28.5b

localize82.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (- (* g g) (* h h)))
27.6b
(sqrt (- (* g g) (* h h)))
8.1b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
2.0b
(- (* g g) (* h h))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×cbrt-prod *-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
6×pow1 times-frac add-log-exp
5×difference-of-squares
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div sub-neg fma-neg pow1/3 diff-log prod-diff div-inv distribute-lft-out--
Counts
4 → 78
Calls
4 calls:
Slowest
19.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
16.0ms
(- (* g g) (* h h))
16.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
395.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
84.0ms
(sqrt (- (* g g) (* h h)))
61.0ms
(sqrt (- (* g g) (* h h)))
42.0ms
(- (* g g) (* h h))

simplify4.4s

Counts
44 → 90
Calls
44 calls:
Slowest
379.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
351.0ms
(- (+ (* 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)))))))))
312.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
268.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
256.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune1.4s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 27.6b

localize57.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (- (* g g) (* h h)))
27.6b
(sqrt (- (* g g) (* h h)))
8.1b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
2.0b
(- (* g g) (* h h))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×cbrt-prod *-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
6×pow1 times-frac add-log-exp
5×difference-of-squares
4×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div sub-neg fma-neg pow1/3 diff-log prod-diff div-inv distribute-lft-out--
Counts
4 → 78
Calls
4 calls:
Slowest
14.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
9.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))
7.0ms
(- (* g g) (* h h))

series541.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
351.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
91.0ms
(sqrt (- (* g g) (* h h)))
56.0ms
(sqrt (- (* g g) (* h h)))
43.0ms
(- (* g g) (* h h))

simplify4.4s

Counts
44 → 90
Calls
44 calls:
Slowest
370.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
359.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
349.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
319.0ms
(- (+ (* 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)))))))))
255.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ -1 a))) (log (/ -1 g))))) (cbrt -1/2))

prune1.7s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 27.6b

localize55.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (- (* g g) (* h h)))
27.6b
(sqrt (- (* g g) (* h h)))
9.0b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
2.0b
(- (* g g) (* h h))

rewrite80.0ms

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
27.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
18.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(sqrt (- (* g g) (* h h)))
15.0ms
(- (* g g) (* h h))

series668.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
464.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
89.0ms
(sqrt (- (* g g) (* h h)))
81.0ms
(sqrt (- (* g g) (* h h)))
33.0ms
(- (* g g) (* h h))

simplify4.4s

Counts
39 → 85
Calls
39 calls:
Slowest
383.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
373.0ms
(fma g g (- (* h h)))
341.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
317.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
300.0ms
(cbrt (* (/ -1/2 a) (+ (pow g 3) (pow (sqrt (- (* g g) (* h h))) 3))))

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 27.6b

regimes737.0ms

Accuracy

60.1% (1.3b remaining)

Error of 31.5b against oracle of 30.2b and baseline of 33.5b

bsearch329.0ms

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.1s3640×body320valid
2.0s4223×body160valid
1.7s7885×body80nan
56.0ms137×body80valid