Details

Time bar (total: 28.5s)

sample136.0ms

Algorithm
intervals
Results
38.0ms118×body320valid
29.0ms265×body80nan
28.0ms132×body160valid
1.0ms6×body80valid

simplify4.5s

Counts
1 → 1
Iterations
IterNodes
done5000
84583
71834
61286
5947
4584
3298
2122
143
019

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.1b

localize82.0ms

Local error

Found 4 expressions with local error:

8.1b
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
9.2b
(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
29.0b
(sqrt (* (+ g h) (- g h)))
29.0b
(sqrt (* (+ g h) (- g h)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
550×times-frac
312×add-sqr-sqrt *-un-lft-identity
226×cbrt-prod
224×add-cube-cbrt
44×distribute-lft-out-- difference-of-squares
21×div-inv
16×sqrt-div
10×frac-times pow1
8×flip3-- flip--
6×cbrt-div flip3-+ associate-*r/ associate-/r/ flip-+
5×associate-*l/
4×sqrt-pow1 add-cbrt-cube add-exp-log add-log-exp
2×pow1/2 pow1/3 pow-prod-down sqrt-prod
Counts
4 → 286
Calls
4 calls:
27.0ms
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
28.0ms
(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
10.0ms
(sqrt (* (+ g h) (- g h)))
21.0ms
(sqrt (* (+ g h) (- g h)))

series1.1s

Counts
4 → 12
Calls
4 calls:
467.0ms
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
447.0ms
(cbrt (/ (- (sqrt (* (+ g h) (- g h))) g) (/ 2.0 (/ 1.0 a))))
92.0ms
(sqrt (* (+ g h) (- g h)))
74.0ms
(sqrt (* (+ g h) (- g h)))

simplify1.1s

Counts
298 → 298
Iterations
IterNodes
done5001
12242
0976

prune3.2s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 30.8b

localize117.0ms

Local error

Found 4 expressions with local error:

2.7b
(cbrt (* (/ (- (sqrt (* (+ h g) (- g h))) g) (sqrt 2.0)) (/ 1.0 (cbrt a))))
8.1b
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
29.0b
(sqrt (* (+ h g) (- g h)))
29.0b
(sqrt (* (+ g h) (- g h)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
11×frac-times
10×pow1
8×cbrt-div flip3-- flip--
7×associate-*r/
6×flip3-+ associate-*l/ flip-+
4×add-sqr-sqrt *-un-lft-identity sqrt-pow1 add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
2×cbrt-prod pow1/2 pow1/3 pow-prod-down sqrt-prod
Counts
4 → 64
Calls
4 calls:
39.0ms
(cbrt (* (/ (- (sqrt (* (+ h g) (- g h))) g) (sqrt 2.0)) (/ 1.0 (cbrt a))))
25.0ms
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
9.0ms
(sqrt (* (+ h g) (- g h)))
9.0ms
(sqrt (* (+ g h) (- g h)))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.1s
(cbrt (* (/ (- (sqrt (* (+ h g) (- g h))) g) (sqrt 2.0)) (/ 1.0 (cbrt a))))
437.0ms
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
81.0ms
(sqrt (* (+ h g) (- g h)))
80.0ms
(sqrt (* (+ g h) (- g h)))

simplify822.0ms

Counts
76 → 76
Iterations
IterNodes
done5000
21952
1522
0244

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 30.6b

localize104.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- g) (sqrt (* (+ g h) (- g h))))
8.1b
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
29.0b
(sqrt (* (- g h) (+ h g)))
29.0b
(sqrt (* (+ g h) (- g h)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
10×frac-times pow1
9×flip3-- flip--
8×*-un-lft-identity add-log-exp
6×add-sqr-sqrt flip3-+ associate-*r/ flip-+
5×cbrt-div associate-*l/
4×sqrt-pow1 add-cbrt-cube add-exp-log add-cube-cbrt
2×pow1/2 diff-log pow-prod-down sqrt-prod distribute-lft-out--
1×associate--l- cbrt-prod neg-sub0 sub-neg distribute-rgt-neg-in pow1/3 neg-log difference-of-squares
Counts
4 → 69
Calls
4 calls:
21.0ms
(- (- g) (sqrt (* (+ g h) (- g h))))
35.0ms
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
25.0ms
(sqrt (* (- g h) (+ h g)))
18.0ms
(sqrt (* (+ g h) (- g h)))

series769.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- g) (sqrt (* (+ g h) (- g h))))
468.0ms
(cbrt (* (/ 1.0 (* a 2.0)) (- (- g) (sqrt (* (+ g h) (- g h))))))
94.0ms
(sqrt (* (- g h) (+ h g)))
96.0ms
(sqrt (* (+ g h) (- g h)))

simplify861.0ms

Counts
81 → 81
Iterations
IterNodes
done5002
21976
1448
0205

prune1.8s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 30.3b

localize145.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (* (- g h) (+ h g))) g)
1.2b
(+ g (sqrt (* (- g h) (+ h g))))
29.0b
(sqrt (* (- g h) (+ h g)))
29.0b
(sqrt (* (- g h) (+ h g)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-div
10×pow1
8×frac-times *-un-lft-identity add-log-exp
7×flip3-+ flip3-- flip-+ flip--
6×add-sqr-sqrt
4×sqrt-pow1 add-cbrt-cube associate-*l/ associate-*r/ add-exp-log add-cube-cbrt
2×pow1/2 pow-prod-down sqrt-prod
1×+-commutative sum-log sub-neg diff-log distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 64
Calls
4 calls:
19.0ms
(- (sqrt (* (- g h) (+ h g))) g)
5.0ms
(+ g (sqrt (* (- g h) (+ h g))))
9.0ms
(sqrt (* (- g h) (+ h g)))
10.0ms
(sqrt (* (- g h) (+ h g)))

series416.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (sqrt (* (- g h) (+ h g))) g)
98.0ms
(+ g (sqrt (* (- g h) (+ h g))))
113.0ms
(sqrt (* (- g h) (+ h g)))
97.0ms
(sqrt (* (- g h) (+ h g)))

simplify2.0s

Counts
76 → 76
Iterations
IterNodes
done5001
34659
2932
1254
0109

prune959.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 30.0b

regimes810.0ms

Accuracy

62.9% (0.9b remaining)

Error of 30.6b against oracle of 29.7b and baseline of 32.3b

bsearch447.0ms

Steps
ItersRangePoint
11
9.11596973352329e-156
1.050264105176939e-135
9.191731187329127e-156

simplify31.0ms

Iterations
IterNodes
done90
490
387
283
178
057

end0.0ms

sample5.8s

Algorithm
intervals
Results
1.6s3719×body320valid
1.6s4125×body160valid
1.6s8101×body80nan
19.0ms156×body80valid