Details

Time bar (total: 7.0s)

sample366.0ms

Algorithm
intervals
Results
42.0ms66×body1280valid
26.0ms262×body80valid
21.0ms48×body640valid
7.0ms23×body320valid
2.0ms9×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize27.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.7b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

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:
4.0ms
(* (atan2 x.im x.re) y.im)
5.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
10.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
157.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune403.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.0b

localize17.0ms

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))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.9b
(* (atan2 x.im x.re) y.im)
29.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite23.0ms

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:
4.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
6.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
6.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series267.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
90.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune349.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im)))
0.0b
(- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im))
0.3b
(* y.re (* 1 (log (hypot x.re x.im))))
1.9b
(* (atan2 x.im x.re) y.im)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×add-exp-log
12×distribute-rgt-in log-prod distribute-lft-in
11×pow1 add-cbrt-cube
10×prod-diff
9×add-log-exp
7×exp-sum
6×associate-*l* prod-exp
5×fma-neg
4×expm1-log1p-u associate-*r* pow-prod-down cbrt-unprod log1p-expm1-u
3×unpow-prod-down exp-prod sqr-pow
2×sub-neg diff-log *-commutative rem-exp-log
1×flip3-- exp-diff 1-exp flip-- unswap-sqr
Counts
4 → 99
Calls
4 calls:
6.0ms
(exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im)))
6.0ms
(- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im))
6.0ms
(* y.re (* 1 (log (hypot x.re x.im))))
4.0ms
(* (atan2 x.im x.re) y.im)

series305.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im)))
129.0ms
(- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im))
77.0ms
(* y.re (* 1 (log (hypot x.re x.im))))
17.0ms
(* (atan2 x.im x.re) y.im)

simplify49.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0391847
11393716
25001673

prune403.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* y.re (* 1 (log (hypot x.re x.im))))
0.4b
(expm1 (exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im))))
0.5b
(log1p (expm1 (exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im)))))
1.9b
(* (atan2 x.im x.re) y.im)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-sqr-sqrt
12×distribute-rgt-in log-prod distribute-lft-in
11×pow1 add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*l* prod-exp
5×log1p-expm1-u
4×expm1-log1p-u associate-*r* pow-prod-down cbrt-unprod add-log-exp
2×*-commutative
1×log1p-udef expm1-log1p 1-exp log1p-expm1 expm1-udef unswap-sqr
Counts
4 → 75
Calls
4 calls:
9.0ms
(* y.re (* 1 (log (hypot x.re x.im))))
1.0ms
(expm1 (exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im))))
1.0ms
(log1p (expm1 (exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im)))))
4.0ms
(* (atan2 x.im x.re) y.im)

series318.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* y.re (* 1 (log (hypot x.re x.im))))
112.0ms
(expm1 (exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im))))
113.0ms
(log1p (expm1 (exp (- (pow (* y.re (* 1 (log (hypot x.re x.im)))) 1) (* (atan2 x.im x.re) y.im)))))
17.0ms
(* (atan2 x.im x.re) y.im)

simplify85.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0337632
11028523
22945512
35001510

prune319.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

regimes210.0ms

Accuracy

0% (0.6b remaining)

Error of 3.8b against oracle of 3.2b and baseline of 3.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02738
13138
23138

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.3s1976×body1280valid
756.0ms8021×body80valid
616.0ms1424×body640valid
186.0ms618×body320valid
59.0ms298×body160valid