Details

Time bar (total: 37.8s)

sample159.0ms

Algorithm
intervals
Results
48.0ms255×body80nan
43.0ms116×body320valid
32.0ms133×body160valid
1.0ms7×body80valid

simplify14.5s

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
01937
14437
212536
331436
463336
5102336
6132536
7162836
8298836
done500136

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize39.0ms

Local error

Found 4 expressions with local error:

7.4b
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
7.6b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.1b
(sqrt (- (* g g) (* h h)))
32.1b
(sqrt (- (* g g) (* h h)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-div
8×add-sqr-sqrt sqrt-prod
6×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u frac-times flip3-- sqrt-div associate-*r/ add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow1/3 associate-*l/ flip-+ difference-of-squares
Counts
4 → 68
Calls
4 calls:
49.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
70.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
23.0ms
(sqrt (- (* g g) (* h h)))
12.0ms
(sqrt (- (* g g) (* h h)))

series1.1s

Counts
4 → 12
Calls
4 calls:
487.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
500.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
66.0ms
(sqrt (- (* g g) (* h h)))
85.0ms
(sqrt (- (* g g) (* h h)))

simplify1.2s

Counts
80 → 80
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01721528
14021345
213591225
done50001180

prune762.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 33.7b

localize50.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (* g g) (* h h))
7.6b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.1b
(sqrt (- (* g g) (* h h)))
32.1b
(sqrt (- (* g g) (* h h)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod
6×pow1 add-cube-cbrt *-un-lft-identity add-log-exp
5×cbrt-div
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube 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 → 69
Calls
4 calls:
9.0ms
(- (* g g) (* h h))
43.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
23.0ms
(sqrt (- (* g g) (* h h)))
24.0ms
(sqrt (- (* g g) (* h h)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* g g) (* h h))
445.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
74.0ms
(sqrt (- (* g g) (* h h)))
58.0ms
(sqrt (- (* g g) (* h h)))

simplify3.4s

Counts
81 → 81
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01461220
13341078
21124960
34776938
done5000938

prune832.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.3b

localize24.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (* g g) (* h h))
7.6b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
32.1b
(sqrt (- (* g g) (* h h)))
32.1b
(sqrt (- (* g g) (* h h)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod
6×pow1 add-cube-cbrt *-un-lft-identity add-log-exp
5×cbrt-div
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube 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 → 69
Calls
4 calls:
20.0ms
(- (* g g) (* h h))
56.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
18.0ms
(sqrt (- (* g g) (* h h)))
18.0ms
(sqrt (- (* g g) (* h h)))

series658.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (* g g) (* h h))
440.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
87.0ms
(sqrt (- (* g g) (* h h)))
73.0ms
(sqrt (- (* g g) (* h h)))

simplify3.1s

Counts
81 → 81
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01461220
13341078
21124960
34776938
done5000938

prune683.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.3b

localize40.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (* g g) (* h h))
7.6b
(cbrt (/ 1.0 (/ (* 2.0 a) (- (sqrt (- (* g g) (* h h))) g))))
32.1b
(sqrt (- (* g g) (* h h)))
32.1b
(sqrt (- (* g g) (* h h)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
41×cbrt-prod
39×add-sqr-sqrt
31×*-un-lft-identity
25×add-cube-cbrt
11×sqrt-prod
9×difference-of-squares
7×associate-/r/
6×pow1 flip3-- flip-- add-log-exp
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u div-inv
3×distribute-lft-out--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg cbrt-div fma-neg pow1/3 diff-log prod-diff
Counts
4 → 105
Calls
4 calls:
13.0ms
(- (* g g) (* h h))
52.0ms
(cbrt (/ 1.0 (/ (* 2.0 a) (- (sqrt (- (* g g) (* h h))) g))))
17.0ms
(sqrt (- (* g g) (* h h)))
17.0ms
(sqrt (- (* g g) (* h h)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* g g) (* h h))
420.0ms
(cbrt (/ 1.0 (/ (* 2.0 a) (- (sqrt (- (* g g) (* h h))) g))))
71.0ms
(sqrt (- (* g g) (* h h)))
75.0ms
(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts
117 → 117
Iterations

Useful iterations: 3 (1.3s)

IterNodesCost
02722457
14892269
213722169
348602144
done50002144

prune741.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.3b

regimes1.1s

Accuracy

67.4% (1.1b remaining)

Error of 31.6b against oracle of 30.4b and baseline of 33.9b

bsearch206.0ms

Steps
ItersRangePoint
9
-3.461821245196587e-165
-7.460550453002327e-171
-3.4219843915306896e-165

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03272
14072
done4072

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s4114×body160valid
1.5s3733×body320valid
1.0s8143×body80nan
15.0ms153×body80valid