Details

Time bar (total: 4.6s)

sample52.0ms

Algorithm
intervals
Results
20.0ms190×body80valid
8.0ms19×body2560valid
6.0ms18×body1280valid
4.0ms8×body5120valid
4.0ms13×body640valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
1.1b
(+ (sqrt (+ (* re re) (* im im))) re)
26.4b
(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 add-cube-cbrt
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 38
Calls
3 calls:
2.0ms
(+ (* re re) (* im im))
13.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* re re) (* im im))
48.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
34.0ms
(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0178275
1689252
22017248
35001246

prune147.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.6b

localize14.0ms

Local error

Found 4 expressions with local error:

3.2b
(exp (log (+ (* re re) (* im im))))
15.7b
(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
26.4b
(sqrt (exp (log (+ (* re re) (* im im)))))
27.5b
(log (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt log-prod
8×pow1 exp-prod
7×exp-sum
6×log-div sqrt-prod add-log-exp
5×add-exp-log sqrt-pow1
4×flip3-+ exp-diff add-cbrt-cube flip-+
3×log-pow
2×rem-sqrt-square sqrt-div
1×+-commutative pow1/2 rem-log-exp sum-log rem-exp-log distribute-lft-out
Counts
4 → 66
Calls
4 calls:
3.0ms
(exp (log (+ (* re re) (* im im))))
19.0ms
(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
6.0ms
(sqrt (exp (log (+ (* re re) (* im im)))))
3.0ms
(log (+ (* re re) (* im im)))

series168.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (log (+ (* re re) (* im im))))
52.0ms
(+ (sqrt (exp (log (+ (* re re) (* im im))))) re)
35.0ms
(sqrt (exp (log (+ (* re re) (* im im)))))
54.0ms
(log (+ (* re re) (* im im)))

simplify63.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (56.0ms)

IterNodesCost
0229555
1716490
21982480
35002473

prune236.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.6b

localize20.0ms

Local error

Found 4 expressions with local error:

15.7b
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (exp (log (+ (* re re) (* im im))))))) re)
27.3b
(cbrt (+ (* re re) (* im im)))
27.3b
(cbrt (exp (log (+ (* re re) (* im im)))))
27.5b
(log (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×log-prod add-log-exp
5×pow1 add-exp-log
4×log-div cbrt-div flip3-+ add-cbrt-cube flip-+
3×exp-sum
2×exp-diff pow1/3
1×+-commutative rem-log-exp sum-log log-pow
Counts
4 → 54
Calls
4 calls:
8.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (exp (log (+ (* re re) (* im im))))))) re)
2.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (exp (log (+ (* re re) (* im im)))))
3.0ms
(log (+ (* re re) (* im im)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (exp (log (+ (* re re) (* im im))))))) re)
95.0ms
(cbrt (+ (* re re) (* im im)))
96.0ms
(cbrt (exp (log (+ (* re re) (* im im)))))
54.0ms
(log (+ (* re re) (* im im)))

simplify106.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0327701
11062624
23526595
35002595

prune316.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.6b

localize18.0ms

Local error

Found 4 expressions with local error:

5.0b
(exp (log (cbrt (+ (* re re) (* im im)))))
16.0b
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
27.3b
(cbrt (+ (* re re) (* im im)))
27.3b
(cbrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div log-prod exp-sum add-log-exp
5×pow1 exp-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3
2×log-div exp-diff log-pow
1×+-commutative sum-log rem-exp-log
Counts
4 → 58
Calls
4 calls:
4.0ms
(exp (log (cbrt (+ (* re re) (* im im)))))
12.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(exp (log (cbrt (+ (* re re) (* im im)))))
81.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (exp (log (cbrt (+ (* re re) (* im im))))))) re)
94.0ms
(cbrt (+ (* re re) (* im im)))
95.0ms
(cbrt (+ (* re re) (* im im)))

simplify100.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0302723
1995653
23237611
35001603

prune331.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.6b

regimes449.0ms

Accuracy

58.6% (8.8b remaining)

Error of 26.2b against oracle of 17.4b and baseline of 38.7b

bsearch135.0ms

Steps
ItersRangePoint
9
1.1927814869807374e+151
9.245727476348249e+156
1.2052644188436986e+151
7
1.4816094939677775e-221
1.6587575435043906e-219
5.275227252356348e-220
7
-3.3580511861940085e-292
-1.4281637648997813e-294
-3.771457836338089e-294

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04826
14826

end0.0ms

sample1.5s

Algorithm
intervals
Results
545.0ms5951×body80valid
314.0ms722×body2560valid
169.0ms482×body1280valid
147.0ms294×body5120valid
85.0ms304×body640valid
35.0ms165×body320valid
12.0ms82×body160valid