Details

Time bar (total: 34.0s)

sample140.0ms

Algorithm
intervals
Results
54.0ms133×body160valid
32.0ms116×body320valid
22.0ms255×body80nan
1.0ms7×body80valid

simplify10.6s

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01937
14337
212236
329736
458336
589136
6107936
7130036
8249136
done500036

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize22.0ms

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)))

rewrite125.0ms

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 frac-times flip3-- sqrt-div associate-*r/ add-cbrt-cube flip-- add-log-exp
2×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow1/3 associate-*l/ flip-+ difference-of-squares
Counts
4 → 60
Calls
4 calls:
47.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
50.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
14.0ms
(sqrt (- (* g g) (* h h)))
10.0ms
(sqrt (- (* g g) (* h h)))

series1.0s

Counts
4 → 12
Calls
4 calls:
452.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
440.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
56.0ms
(sqrt (- (* g g) (* h h)))
52.0ms
(sqrt (- (* g g) (* h h)))

simplify3.1s

Counts
72 → 72
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01661416
13851249
212681135
349571078
done50001076

prune700.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 33.7b

localize35.0ms

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)))

rewrite94.0ms

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 sqrt-div add-cbrt-cube
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 pow1/3 diff-log associate-*l/
Counts
4 → 59
Calls
4 calls:
17.0ms
(- (* g g) (* h h))
52.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
12.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series714.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* g g) (* h h))
480.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
92.0ms
(sqrt (- (* g g) (* h h)))
95.0ms
(sqrt (- (* g g) (* h h)))

simplify3.0s

Counts
71 → 71
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01371112
1317990
21031876
34329853
done5001842

prune643.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.3b

localize22.0ms

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)))

rewrite114.0ms

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 sqrt-div add-cbrt-cube
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 pow1/3 diff-log associate-*l/
Counts
4 → 59
Calls
4 calls:
15.0ms
(- (* g g) (* h h))
68.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
19.0ms
(sqrt (- (* g g) (* h h)))
9.0ms
(sqrt (- (* g g) (* h h)))

series650.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* g g) (* h h))
451.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
69.0ms
(sqrt (- (* g g) (* h h)))
84.0ms
(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts
71 → 71
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01371112
1317990
21031876
34329853
done5001842

prune614.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 32.3b

localize52.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (* g g) (* h h))
7.4b
(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)))

rewrite106.0ms

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 flip3-- flip--
4×add-exp-log sqrt-div add-cbrt-cube
3×difference-of-squares
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
1×cbrt-prod sub-neg pow1/3 diff-log associate-*l/
Counts
4 → 59
Calls
4 calls:
16.0ms
(- (* g g) (* h h))
56.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
16.0ms
(sqrt (- (* g g) (* h h)))
16.0ms
(sqrt (- (* g g) (* h h)))

series538.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* g g) (* h h))
360.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
80.0ms
(sqrt (- (* g g) (* h h)))
64.0ms
(sqrt (- (* g g) (* h h)))

simplify2.4s

Counts
71 → 71
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01351112
1294991
2968887
33952865
done5000855

prune504.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.3b

regimes1.2s

Accuracy

68.9% (1.1b remaining)

Error of 31.6b against oracle of 30.5b and baseline of 34.1b

bsearch248.0ms

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

simplify27.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03678
14476
done4476

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.4s4114×body160valid
1.3s3733×body320valid
1.3s8143×body80nan
14.0ms153×body80valid