Details

analyze1.5s (13.7%)

Algorithm

1×

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample115.0ms (1%)

Algorithm

1×

intervals

Results

45.0ms	81×	body	1024	invalid
33.0ms	242×	body	128	valid
5.0ms	5×	body	2048	invalid
3.0ms	13×	body	256	invalid
3.0ms	8×	body	512	invalid
2.0ms	4×	body	1024	valid
2.0ms	6×	body	512	valid
1.0ms	1×	body	2048	valid
1.0ms	6×	body	128	invalid
1.0ms	3×	body	256	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify163.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.8b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 (atan2.f64 x.im x.re) y.im)
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.6b	(sin.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)))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

8.0ms	(sin.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)

series643.0ms (5.8%)

Counts

4 → 56

Calls

4 calls:

311.0ms	(sin.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)))
146.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
111.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3792 to 2504 computations (34% saved)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4982	2268
1	4982	2268

prune180.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Error

15.4b

Counts

114 → 9

Compiler

Compiled 4925 to 1423 computations (71.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.6b	(sin.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)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

7.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
7.0ms	(sin.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)))

series932.0ms (8.5%)

Counts

4 → 56

Calls

4 calls:

371.0ms	(.f64 (atan2.f64 x.im x.re) (.f64 (cbrt.f64 y.im) (cbrt.f64 y.im)))
297.0ms	(sin.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)))
149.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
115.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4433 to 2843 computations (35.9% saved)

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5122	2417

prune172.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	113	9	122

Error

15.4b

Counts

122 → 9

Compiler

Compiled 5747 to 1571 computations (72.7% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.9b	(cbrt.f64 (atan2.f64 x.im x.re))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.6b	(sin.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)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cbrt-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow1/3_binary64` `sin-sum_binary64`

Counts

4 → 49

Calls

4 calls:

6.0ms	(sin.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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

series772.0ms (7%)

Counts

4 → 53

Calls

4 calls:

304.0ms	(sin.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)))
210.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
145.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
113.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 4993 to 2995 computations (40% saved)

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4962	2124
1	4962	2124

prune191.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Error

15.4b

Counts

111 → 9

Compiler

Compiled 6278 to 2027 computations (67.7% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.9b	(cbrt.f64 (atan2.f64 x.im x.re))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.7b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
34.6b	(sin.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)))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cbrt-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow1/3_binary64` `sin-sum_binary64`

Counts

4 → 49

Calls

4 calls:

6.0ms	(sin.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)))
1.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

series796.0ms (7.2%)

Counts

4 → 53

Calls

4 calls:

312.0ms	(sin.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)))
200.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
161.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
123.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 6072 to 3256 computations (46.4% saved)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4962	2124
1	4962	2124

prune203.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	101	10	111

Error

15.4b

Counts

111 → 10

Compiler

Compiled 7200 to 1797 computations (75% saved)

regimes501.0ms (4.6%)

Accuracy

Total 0.3b remaining (1.4%)

Threshold costs 0.3b (1.4%)

Compiler

Compiled 5842 to 3560 computations (39.1% saved)

bsearch4.0ms (0%)

Compiler: Compiled 37 to 19 computations (48.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	221
1	80	221

end0.0ms (0%)

sample4.3s (39.2%)

Algorithm

1×

intervals

Results

1.3s	2489×	body	1024	invalid
897.0ms	7581×	body	128	valid
340.0ms	921×	body	512	invalid
160.0ms	183×	body	2048	invalid
96.0ms	183×	body	1024	valid
81.0ms	343×	body	256	invalid
62.0ms	493×	body	128	invalid
51.0ms	142×	body	512	valid
19.0ms	81×	body	256	valid
10.0ms	13×	body	2048	valid

Compiler

Compiled 1303 to 766 computations (41.2% saved)

Details

analyze1.5s (13.7%)

sample115.0ms (1%)

simplify163.0ms (1.5%)

prune9.0ms (0.1%)

localize32.0ms (0.3%)

rewrite28.0ms (0.3%)

series643.0ms (5.8%)

simplify77.0ms (0.7%)

prune180.0ms (1.6%)

localize25.0ms (0.2%)

rewrite29.0ms (0.3%)

series932.0ms (8.5%)

simplify79.0ms (0.7%)

prune172.0ms (1.6%)

localize30.0ms (0.3%)

rewrite23.0ms (0.2%)

series772.0ms (7%)

simplify58.0ms (0.5%)

prune191.0ms (1.7%)

localize38.0ms (0.3%)

rewrite24.0ms (0.2%)

series796.0ms (7.2%)

simplify61.0ms (0.6%)

prune203.0ms (1.8%)

regimes501.0ms (4.6%)

bsearch4.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.3s (39.2%)

Profiling