Details

Time bar (total: 5.7s)

sample310.0ms

Algorithm
intervals
Results
22.0ms251×body80valid
10.0ms133×body80overflowed
4.0ms7×body1280valid
3.0ms6×body640valid
1.0ms3×body320valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.re)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
21.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.re)
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
147.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify79.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0205456
1546415
21264411
32748411
45001411

prune364.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.2b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.2b
(* (atan2 x.im x.re) y.im)
30.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ hypot-def
Counts
4 → 77
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
14.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
86.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify89.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune315.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
1.2b
(* (atan2 x.im x.re) y.im)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow1/3 associate-*r* associate-*l*
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 59
Calls
4 calls:
1.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
10.0ms
(* (atan2 x.im x.re) y.im)

series537.0ms

Counts
4 → 12
Calls
4 calls:
172.0ms
(cbrt y.re)
175.0ms
(cbrt y.re)
174.0ms
(cbrt y.re)
15.0ms
(* (atan2 x.im x.re) y.im)

simplify62.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (19.0ms)

IterNodesCost
0102209
1300190
2710184
31530181
45001181

prune294.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y.re)
0.6b
(cbrt y.re)
1.2b
(* (atan2 x.im x.re) y.im)
1.6b
(expm1 (log1p (* (atan2 x.im x.re) y.im)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log cbrt-prod add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×pow1/3
1×expm1-log1p pow-prod-down prod-exp *-commutative cbrt-unprod expm1-udef unswap-sqr
Counts
4 → 57
Calls
4 calls:
1.0ms
(cbrt y.re)
1.0ms
(cbrt y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
0.0ms
(expm1 (log1p (* (atan2 x.im x.re) y.im)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt y.re)
171.0ms
(cbrt y.re)
19.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(expm1 (log1p (* (atan2 x.im x.re) y.im)))

simplify55.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (18.0ms)

IterNodesCost
0114208
1316187
2728183
31547181
45002181

prune287.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

regimes204.0ms

Accuracy

43.5% (2.0b remaining)

Error of 5.6b against oracle of 3.6b and baseline of 7.2b

bsearch325.0ms

Steps
ItersRangePoint
9
2.5581394584366297e+228
1.9970187604071902e+235
2.4635477106731157e+232
11
8.177335258021847e+131
8.387333684259973e+162
7.159178655710649e+162
8
-8.27319011390235e+81
-8.554578510292574e+78
-6.384605674813404e+81

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
04256
15126
25426
35426

end0.0ms

sample1.6s

Algorithm
intervals
Results
663.0ms7977×body80valid
315.0ms3940×body80overflowed
83.0ms138×body1280valid
66.0ms163×body640valid
29.0ms108×body320valid
11.0ms63×body160valid