Details

Time bar (total: 5.2s)

sample69.0ms

Algorithm
intervals
Results
19.0ms117×body320valid
17.0ms246×body80nan
15.0ms136×body160valid
0.0ms3×body80valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01937
14437
212236
330136
457436
588536
6115436
7142836
8297936
done500036

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize17.0ms

Local error

Found 4 expressions with local error:

6.5b
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
8.2b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.1b
(sqrt (- (* g g) (* h h)))
31.1b
(sqrt (- (* g g) (* h h)))

rewrite44.0ms

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:
17.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
17.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms
(sqrt (- (* g g) (* h h)))
5.0ms
(sqrt (- (* g g) (* h h)))

series705.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))
315.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
43.0ms
(sqrt (- (* g g) (* h h)))
48.0ms
(sqrt (- (* g g) (* h h)))

simplify465.0ms

Counts
80 → 80
Iterations

Useful iterations: done (462.0ms)

IterNodesCost
01721528
14071345
214201225
done50001188

prune436.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 32.4b

localize23.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* g g) (* h h))
8.2b
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
31.1b
(sqrt (- (* g g) (* h h)))
31.1b
(sqrt (- (* g g) (* h h)))

rewrite30.0ms

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:
3.0ms
(- (* g g) (* h h))
17.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
4.0ms
(sqrt (- (* g g) (* h h)))
5.0ms
(sqrt (- (* g g) (* h h)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* g g) (* h h))
307.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))
48.0ms
(sqrt (- (* g g) (* h h)))
46.0ms
(sqrt (- (* g g) (* h h)))

simplify447.0ms

Counts
81 → 81
Iterations

Useful iterations: done (445.0ms)

IterNodesCost
01461220
13471078
21294960
done5001953

prune482.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 31.9b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* g g) (* h h))
1.4b
(- (* g g) (* h h))
31.1b
(sqrt (- (* g g) (* h h)))
31.1b
(sqrt (- (* g g) (* h h)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt sqrt-prod add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 70
Calls
4 calls:
3.0ms
(- (* g g) (* h h))
3.0ms
(- (* g g) (* h h))
5.0ms
(sqrt (- (* g g) (* h h)))
4.0ms
(sqrt (- (* g g) (* h h)))

series160.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(- (* g g) (* h h))
36.0ms
(- (* g g) (* h h))
44.0ms
(sqrt (- (* g g) (* h h)))
50.0ms
(sqrt (- (* g g) (* h h)))

simplify157.0ms

Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
062912
1136824
2466722