Details

analyze1.6s (15.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5006	504
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample110.0ms (1.1%)

Algorithm

1×

intervals

Results

36.0ms	61×	body	1024	invalid
27.0ms	239×	body	128	valid
9.0ms	25×	body	512	invalid
5.0ms	9×	body	1024	valid
3.0ms	25×	body	128	invalid
3.0ms	12×	body	256	invalid
2.0ms	5×	body	512	valid
2.0ms	2×	body	2048	invalid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

34.9b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite104.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

34.9b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series624.0ms (6%)

Error

22.3b

Counts

4 → 51

Calls

4 calls:

246.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
144.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
95.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
73.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5292 to 2678 computations (49.4% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5151	2028

prune154.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	100	7	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	7	108

Error

22.3b

Counts

108 → 7

Compiler

Compiled 4579 to 1246 computations (72.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.7b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
30.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite78.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

22.3b

Rules

14×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`sqrt-div_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
1.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series436.0ms (4.2%)

Error

3.9b

Counts

4 → 45

Calls

4 calls:

134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
118.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
70.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
69.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3270 to 1723 computations (47.3% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5145	1447

prune119.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Error

3.9b

Counts

110 → 10

Compiler

Compiled 3227 to 847 computations (73.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.7b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite69.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

16×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
9×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`log-pow_binary64`

Counts

4 → 62

Calls

4 calls:

5.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1541 to 323 computations (79% saved)

series474.0ms (4.6%)

Error

3.9b

Counts

4 → 36

Calls

4 calls:

188.0ms	(*.f64 (log.f64 (neg.f64 x.re)) y.re)
127.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
68.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
66.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2107 to 1119 computations (46.9% saved)

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4967	1283
1	4967	1283

prune88.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	98	10	108

Error

3.9b

Counts

108 → 10

Compiler

Compiled 2505 to 560 computations (77.6% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
30.5b	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
30.5b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.7b	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))

rewrite132.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

3.9b

Rules

12×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `distribute-lft-out_binary64`
1×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
6.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2850 to 1225 computations (57% saved)

series652.0ms (6.3%)

Error

3.9b

Counts

4 → 51

Calls

4 calls:

239.0ms	(cos.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))))))
151.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
98.0ms	(sqrt.f64 (+.f64 (pow.f64 x.im 2) (pow.f64 x.re 2)))
85.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5697 to 3533 computations (38% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5179	2058

prune186.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	109	10	119

Error

3.9b

Counts

119 → 10

Compiler

Compiled 4703 to 2064 computations (56.1% saved)

regimes647.0ms (6.2%)

Accuracy

Total 5.5b remaining (61.3%)

Threshold costs 0b (0%)

Compiler

Compiled 6732 to 4275 computations (36.5% saved)

bsearch93.0ms (0.9%)

Steps

Iters	Range		Point
8	-3.816229993685747e-305	1.658577703816624e-308	-1.4701993751772e-310

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	81
1	65	81

end0.0ms (0%)

sample4.4s (42.5%)

Algorithm

1×

intervals

Results

1.3s	2521×	body	1024	invalid
840.0ms	7579×	body	128	valid
348.0ms	982×	body	512	invalid
104.0ms	435×	body	256	invalid
96.0ms	188×	body	1024	valid
65.0ms	572×	body	128	invalid
44.0ms	127×	body	512	valid
30.0ms	36×	body	2048	invalid
24.0ms	90×	body	256	valid
13.0ms	16×	body	2048	valid

Compiler

Compiled 1409 to 887 computations (37% saved)

Details

analyze1.6s (15.1%)

sample110.0ms (1.1%)

simplify63.0ms (0.6%)

prune8.0ms (0.1%)

localize30.0ms (0.3%)

rewrite104.0ms (1%)

series624.0ms (6%)

simplify72.0ms (0.7%)

prune154.0ms (1.5%)

localize18.0ms (0.2%)

rewrite78.0ms (0.8%)

series436.0ms (4.2%)

simplify65.0ms (0.6%)

prune119.0ms (1.1%)

localize13.0ms (0.1%)

rewrite69.0ms (0.7%)

series474.0ms (4.6%)

simplify63.0ms (0.6%)

prune88.0ms (0.8%)

localize29.0ms (0.3%)

rewrite132.0ms (1.3%)

series652.0ms (6.3%)

simplify72.0ms (0.7%)

prune186.0ms (1.8%)

regimes647.0ms (6.2%)

bsearch93.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.4s (42.5%)

Profiling