Details

Time bar (total: 4.3s)

sample24.0ms

Algorithm
intervals
Results
6.0ms201×body80valid
5.0ms25×body2560valid
2.0ms7×body5120valid
2.0ms10×body1280valid
1.0ms10×body640valid
0.0ms2×body320valid
0.0ms1×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0248
1308
2338
3338

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
31.8b
(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
7×pow1 add-sqr-sqrt sqrt-prod
6×add-cube-cbrt fma-def
5×add-log-exp
4×sqrt-div
3×add-exp-log expm1-log1p-u sqrt-pow1 flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log hypot-def distribute-lft-out
Counts
3 → 53
Calls
3 calls:
8.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
7.0ms
(sqrt (+ (* re re) (* im im)))

series267.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
50.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0264372
1830337
22660322
35002320

prune179.0ms

Filtered
62 candidates to 56 candidates (90.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (hypot re im) re)))
0.3b
(+ (hypot re im) re)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1 *-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def
2×add-exp-log expm1-log1p-u sqrt-pow1 flip3-+ sqrt-div associate-*r/ add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative pow1/2 pow-prod-down sum-log sqrt-prod distribute-lft-out
Counts
2 → 32
Calls
2 calls:
5.0ms
(sqrt (* 2.0 (+ (hypot re im) re)))
3.0ms
(+ (hypot re im) re)

series252.0ms

Counts
2 → 6
Calls
2 calls:
192.0ms
(sqrt (* 2.0 (+ (hypot re im) re)))
60.0ms
(+ (hypot re im) re)

simplify50.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0183173
1519156
21741150
35001148

prune106.0ms

Filtered
38 candidates to 34 candidates (89.5%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (sqrt (* 2.0 (+ (hypot re im) re)))) (cbrt (sqrt (* 2.0 (+ (hypot re im) re)))))
0.4b
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
0.4b
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
0.4b
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod
23×add-sqr-sqrt
20×associate-*r/
18×cbrt-div sqrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
7×swap-sqr associate-*r* associate-*l* sqrt-prod
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 101
Calls
4 calls:
9.0ms
(* (cbrt (sqrt (* 2.0 (+ (hypot re im) re)))) (cbrt (sqrt (* 2.0 (+ (hypot re im) re)))))
5.0ms
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
5.0ms
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
5.0ms
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))

series1.5s

Counts
4 → 12
Calls
4 calls:
385.0ms
(* (cbrt (sqrt (* 2.0 (+ (hypot re im) re)))) (cbrt (sqrt (* 2.0 (+ (hypot re im) re)))))
448.0ms
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
310.0ms
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))
320.0ms
(cbrt (sqrt (* 2.0 (+ (hypot re im) re))))

simplify52.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03521340
112001257
250021182

prune370.0ms

Filtered
113 candidates to 89 candidates (78.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
13.5b
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×pow1
2×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity sqrt-pow1 add-cbrt-cube log1p-expm1-u add-log-exp
1×pow1/2 pow-prod-down sqrt-prod fma-udef
Counts
2 → 23
Calls
2 calls:
3.0ms
(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
1.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

series383.0ms

Counts
2 → 6
Calls
2 calls:
244.0ms
(sqrt (* 2.0 (fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)))
139.0ms
(fma (sqrt (hypot re im)) (sqrt (hypot re im)) re)

simplify44.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0129225
1378193
21445178
35002174

prune81.0ms

Filtered
29 candidates to 24 candidates (82.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.3b

regimes73.0ms

Accuracy

30.3% (4.1b remaining)

Error of 11.5b against oracle of 7.4b and baseline of 13.3b

bsearch73.0ms

Steps
ItersRangePoint
7
-1.0114733541290617e-38
-2.5734052351795068e-40
-9.259771162716737e-39
3
-1.4509995558059801e+125
-1.140406744705429e+125
-1.2762910995619203e+125
2
-6.814808586201778e+164
-5.701746713112747e+164
-5.840879447248876e+164

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
03224
13512
23812
33812

end0.0ms

sample659.0ms

Algorithm
intervals
Results
196.0ms6029×body80valid
133.0ms715×body2560valid
71.0ms471×body1280valid
63.0ms270×body5120valid
44.0ms281×body640valid
14.0ms151×body320valid
5.0ms83×body160valid