Details

Time bar (total: 33.7s)

sample134.0ms

Algorithm
intervals
Results
44.0ms117×body320valid
28.0ms294×body80nan
26.0ms136×body160valid
0.0ms3×body80valid

simplify9.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
01937
14337
212236
329736
458336
589136
6107936
7130036
8249136
done500036

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize30.0ms

Local error

Found 4 expressions with local error:

5.5b
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
5.8b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.0b
(sqrt (- (* g g) (* h h)))
31.0b
(sqrt (- (* g g) (* h h)))

rewrite131.0ms

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:
55.0ms
(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)))

series932.0ms

Counts
4 → 12
Calls
4 calls:
400.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
405.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
67.0ms
(sqrt (- (* g g) (* h h)))
60.0ms
(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts
72 → 72
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01661416
13851249
212681135
349571078
done50001076

prune619.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 32.6b

localize43.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (* g g) (* h h))
5.8b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.0b
(sqrt (- (* g g) (* h h)))
31.0b
(sqrt (- (* g g) (* h h)))

rewrite95.0ms

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))
44.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
18.0ms
(sqrt (- (* g g) (* h h)))
15.0ms
(sqrt (- (* g g) (* h h)))

series676.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* g g) (* h h))
470.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
83.0ms
(sqrt (- (* g g) (* h h)))
79.0ms
(sqrt (- (* g g) (* h h)))

simplify2.6s

Counts
71 → 71
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01371112
1317990
21031876
34329853
done5001842

prune594.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 31.6b

localize34.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (* g g) (* h h))
5.8b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.0b
(sqrt (- (* g g) (* h h)))
31.0b
(sqrt (- (* g g) (* h h)))

rewrite90.0ms

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:
12.0ms
(- (* g g) (* h h))
45.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
17.0ms
(sqrt (- (* g g) (* h h)))
13.0ms
(sqrt (- (* g g) (* h h)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* g g) (* h h))
403.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
75.0ms
(sqrt (- (* g g) (* h h)))
57.0ms
(sqrt (- (* g g) (* h h)))

simplify3.6s

Counts
71 → 71
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01371112
1317990
21031876
34329853
done5001842

prune650.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 31.6b

localize26.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (* g g) (* h h))
5.5b
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
31.0b
(sqrt (- (* g g) (* h h)))
31.0b
(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 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:
15.0ms
(- (* g g) (* h h))
53.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
13.0ms
(sqrt (- (* g g) (* h h)))
10.0ms
(sqrt (- (* g g) (* h h)))

series604.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* g g) (* h h))
412.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
73.0ms
(sqrt (- (* g g) (* h h)))
62.0ms
(sqrt (- (* g g) (* h h)))

simplify2.5s

Counts
71 → 71
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01351112
1294991
2968887
33952865
done5000855

prune575.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 31.6b

regimes1.3s

Accuracy

80.1% (1.1b remaining)

Error of 31.9b against oracle of 30.7b and baseline of 36.5b

bsearch274.0ms

Steps
ItersRangePoint
10
-2.2642462469951956e-148
-5.565598515937264e-162
-2.4223450526411114e-160

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03393
14293
done4293

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.3s3693×body320valid
1.3s7970×body80nan
1.2s4152×body160valid
17.0ms155×body80valid