Details

Time bar (total: 37.0s)

sample195.0ms

Algorithm
intervals
Results
86.0ms124×body320valid
46.0ms126×body160valid
41.0ms260×body80nan
1.0ms6×body80valid

simplify343.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
342.0ms
(+ (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: 33.0b

localize36.0ms

Local error

Found 4 expressions with local error:

27.1b
(sqrt (- (* g g) (* h h)))
27.1b
(sqrt (- (* g g) (* h h)))
8.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
8.1b
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))

rewrite79.0ms

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)))
26.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
14.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series868.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
441.0ms
(cbrt (* (/ -1/2 a) (+ g (sqrt (- (* g g) (* h h))))))
308.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
63.0ms
(sqrt (- (* g g) (* h h)))
55.0ms
(sqrt (- (* g g) (* h h)))

simplify6.4s

Counts
45 → 89
Calls
45 calls:
Slowest
443.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
389.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ 1 a))) (log (/ 1 g))))) (cbrt -1/2))
367.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
323.0ms
(- (+ (* 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)))))))))
299.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.0b

localize52.0ms

Local error

Found 4 expressions with local error:

27.1b
(sqrt (- (* g g) (* h h)))
27.1b
(sqrt (- (* g g) (* h h)))
8.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
3.0b
(- (* g g) (* h h))

rewrite66.0ms

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
29.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
15.0ms
(- (* g g) (* h h))
11.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
325.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
54.0ms
(sqrt (- (* g g) (* h h)))
49.0ms
(sqrt (- (* g g) (* h h)))
43.0ms
(- (* g g) (* h h))

simplify4.6s

Counts
44 → 90
Calls
44 calls:
Slowest
395.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
359.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
314.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
308.0ms
(- (+ (* 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)))))))))
291.0ms
(* (exp (* 1/3 (- (+ (log 2) (log (/ -1 a))) (log (/ -1 g))))) (cbrt -1/2))

prune1.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.5b

localize61.0ms

Local error

Found 4 expressions with local error:

27.1b
(sqrt (- (* g g) (* h h)))
27.1b
(sqrt (- (* g g) (* h h)))
3.0b
(- (* g g) (* h h))
3.0b
(- (* g g) (* h h))

rewrite49.0ms

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
15.0ms
(- (* g g) (* h h))
15.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(- (* g g) (* h h))

series218.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(sqrt (- (* g g) (* h h)))
54.0ms
(sqrt (- (* g g) (* h h)))
44.0ms
(- (* g g) (* h h))
41.0ms
(- (* g g) (* h h))

simplify2.5s

Counts
38 → 86
Calls
38 calls:
Slowest
312.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
290.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
240.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))
224.0ms
(/ (exp (* g g)) (exp (* h h)))
212.0ms
(sqrt (- (pow (* g g) 3) (pow (* h h) 3)))

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.4b

localize62.0ms

Local error

Found 4 expressions with local error:

27.1b
(sqrt (- (* g g) (* h h)))
27.1b
(sqrt (- (* g g) (* h h)))
8.4b
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
3.0b
(- (* g g) (* h h))

rewrite80.0ms

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
28.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
19.0ms
(sqrt (- (* g g) (* h h)))
19.0ms
(sqrt (- (* g g) (* h h)))
13.0ms
(- (* g g) (* h h))

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
351.0ms
(cbrt (/ (- (sqrt (- (* g g) (* h h))) g) (* a 2)))
72.0ms
(sqrt (- (* g g) (* h h)))
61.0ms
(sqrt (- (* g g) (* h h)))
38.0ms
(- (* g g) (* h h))

simplify5.1s

Counts
44 → 90
Calls
44 calls:
Slowest
552.0ms
(sqrt (* (cbrt (- (* g g) (* h h))) (cbrt (- (* g g) (* h h)))))
484.0ms
(* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (+ (log (/ 1 g)) (log -1/2))) (* 2 (log (/ 1 h)))))))
374.0ms
(- (+ (* 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)))))))))
311.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))
302.0ms
(sqrt (- (* (* g g) (* g g)) (* (* h h) (* h h))))

prune1.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 27.4b

regimes841.0ms

Accuracy

55.1% (1.4b remaining)

Error of 30.8b against oracle of 29.4b and baseline of 32.6b

bsearch202.0ms

end0.0ms

sample7.9s

Algorithm
intervals
Results
2.7s8263×body80nan
2.7s3687×body320valid
2.1s4157×body160valid
29.0ms156×body80valid