Details

Time bar (total: 6.8s)

sample344.0ms

Algorithm
intervals
Results
26.0ms45×body1280valid
23.0ms260×body80valid
13.0ms34×body640valid
7.0ms25×body320valid
1.0ms6×body160valid

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.6b

localize25.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
31.9b
(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)))

rewrite21.0ms

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×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
38.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
151.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0189422
1491385
21112381
32393381
45001381

prune310.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (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)
1.0b
(* (atan2 x.im x.re) y.im)
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×pow1
10×add-cube-cbrt *-un-lft-identity
9×associate-*l*
8×add-exp-log add-cbrt-cube
7×add-log-exp
6×associate-*r*
3×exp-prod sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div exp-sum pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
1×sub-neg rem-sqrt-square flip3-+ exp-diff diff-log flip-+
Counts
4 → 69
Calls
4 calls:
11.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im)))
93.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify58.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0280545
1825486
22118481
35001481

prune286.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ -1 x.re) y.re)
0.0b
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
0.0b
(exp (- (* (atan2 x.im x.re) y.im)))
1.0b
(* (atan2 x.im x.re) y.im)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
67×add-sqr-sqrt
65×add-cube-cbrt unpow-prod-down *-un-lft-identity
17×associate-/r*
13×add-exp-log
8×add-cbrt-cube
7×pow1
6×exp-prod div-exp div-inv add-log-exp
5×sqr-pow
4×pow-exp
3×pow-unpow associate-*r* associate-*l* associate-/l*
2×neg-sub0 exp-neg pow-to-exp exp-diff rem-exp-log associate-/l/
1×cbrt-undiv distribute-lft-neg-in neg-mul-1 pow-pow distribute-rgt-neg-in frac-2neg pow-prod-down neg-log prod-exp clear-num *-commutative cbrt-unprod unswap-sqr
Counts
4 → 151
Calls
4 calls:
3.0ms
(pow (/ -1 x.re) y.re)
11.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
2.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
3.0ms
(* (atan2 x.im x.re) y.im)

series190.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (/ -1 x.re) y.re)
91.0ms
(/ (exp (- (* (atan2 x.im x.re) y.im))) (pow (/ -1 x.re) y.re))
23.0ms
(exp (- (* (atan2 x.im x.re) y.im)))
16.0ms
(* (atan2 x.im x.re) y.im)

simplify62.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
05341633
121761576
250021576

prune540.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
1.0b
(* (atan2 x.im x.re) y.im)
2.2b
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
31.9b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×pow1
8×add-exp-log log-pow add-cbrt-cube
7×associate-*l*
6×exp-prod associate-*r* sqrt-prod
4×add-log-exp
3×log-prod
2×sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 70
Calls
4 calls:
3.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
7.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series184.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (log (log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))) y.re)
17.0ms
(* (atan2 x.im x.re) y.im)
40.0ms
(log (exp (sqrt (+ (* x.re x.re) (* x.im x.im)))))
35.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify103.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0256510
1732441
21709432
33785432
45002432

prune285.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 2.5b

regimes301.0ms

Accuracy

64.7% (9.2b remaining)

Error of 13.5b against oracle of 4.2b and baseline of 30.4b

bsearch327.0ms

Steps
ItersRangePoint
8
1.2456874397123594e-21
5.409776585196184e-17
1.2712943529250103e-21
4
2.1762361612367286e-91
3.4110694680957845e-91
3.3637837218998096e-91
5
-1.0680487192983464e-308
2.5344995100410685e-308
1.457786286792e-311
4
-3.072988850476841e-182
-2.125016143058441e-182
-3.015633963110011e-182
6
-8.315349989810019e-23
-9.449337279958446e-24
-1.703724525594636e-23

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07463
18263
28263

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s2007×body1280valid
674.0ms7993×body80valid
543.0ms1405×body640valid
165.0ms614×body320valid
56.0ms315×body160valid