Details

analyze2.0s (11.2%)

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

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample161.0ms (0.9%)

Algorithm

1×

intervals

Results

59.0ms	89×	body	1024	invalid
34.0ms	238×	body	128	valid
17.0ms	29×	body	512	invalid
5.0ms	5×	body	2048	invalid
5.0ms	14×	body	256	invalid
4.0ms	6×	body	1024	valid
3.0ms	19×	body	128	invalid
3.0ms	7×	body	256	valid
3.0ms	5×	body	512	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify64.0ms (0.4%)

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%)

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

36.1b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.8b	(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)))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite103.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

36.0b

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×	`sin-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

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)))
6.0ms	(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)

series983.0ms (5.6%)

Error

22.4b

Counts

4 → 58

Calls

4 calls:

473.0ms	(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)))
178.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
144.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
95.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 6356 to 3225 computations (49.3% saved)

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5050	2475

prune199.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	106	8	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Error

22.4b

Counts

115 → 9

Compiler

Compiled 5034 to 1394 computations (72.3% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

32.0b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite316.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

22.4b

Rules

20×	`*-un-lft-identity_binary64`
18×	`sqrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
6×	`unpow-prod-down_binary64` `distribute-lft-out_binary64`
4×	`pow1/2_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 66

Calls

4 calls:

11.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 5748 to 2873 computations (50% saved)

series946.0ms (5.4%)

Error

22.4b

Counts

4 → 62

Calls

4 calls:

191.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
183.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
175.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
163.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 12113 to 7118 computations (41.2% saved)

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5052	2209

prune600.0ms (3.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	126	11	137

Error

22.4b

Counts

137 → 11

Compiler

Compiled 10882 to 5424 computations (50.2% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

14.3b	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))))) 3))
29.8b	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.0b	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

rewrite194.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

22.4b

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
8×	`sqrt-prod_binary64`
6×	`pow1_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cube-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `distribute-lft-out_binary64` `rem-sqrt-square_binary64`
1×	`sin-sum_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64`

Counts

4 → 61

Calls

4 calls:

10.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))))) 3))
9.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 3307 to 1470 computations (55.5% saved)

series1.3s (7.4%)

Error

22.4b

Counts

4 → 65

Calls

4 calls:

460.0ms	(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))))))) 3))
371.0ms	(sin.f64 (+.f64 (.f64 y.re (atan2.f64 x.im x.re)) (.f64 y.im (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))))))
164.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
161.0ms	(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))

Compiler

Compiled 7637 to 4434 computations (41.9% saved)

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4956	3742
1	4956	3742

prune321.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	124	13	137

Error

22.4b

Counts

137 → 13

Compiler

Compiled 6131 to 2607 computations (57.5% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.5b	(*.f64 (atan2.f64 x.im x.re) y.im)
16.8b	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
22.4b	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3))
32.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite109.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

22.4b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-l_binary64` `associate-r_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3))
2.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 2218 to 548 computations (75.3% saved)

series609.0ms (3.5%)

Error

14.5b

Counts

4 → 47

Calls

4 calls:

167.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
163.0ms	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 y.re (atan2.f64 x.im x.re))) 3))
136.0ms	(sin.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
89.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3753 to 2123 computations (43.4% saved)

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5099	1719

prune137.0ms (0.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	1	9	10
Picked	1	0	1
Done	0	2	2
Total	106	15	121

Error

14.5b

Counts

121 → 15

Compiler

Compiled 3342 to 898 computations (73.1% saved)

regimes1.6s (9.1%)

Accuracy

Total 9.6b remaining (42.9%)

Threshold costs 0b (0%)

Compiler

Compiled 14627 to 9240 computations (36.8% saved)

bsearch460.0ms (2.6%)

Steps

Iters	Range		Point
6	1.798301029127406e+54	7.925587002278094e+54	3.830449135996521e+54
9	279.84913426541436	930935118.0435365	72273.62012139842
7	4.329247734157589e-174	1.1560899359757212e-172	1.4724929191929907e-173
10	-8.991598433474235e-114	-3.20204909375144e-125	-7.152265036082887e-122
9	-1.3070488064622128e+146	-5.359028552902453e+138	-4.6754114793960554e+144

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	108	375
1	108	375

end0.0ms (0%)

sample6.8s (39.2%)

Algorithm

1×

intervals

Results

1.5s	2429×	body	1024	invalid
1.1s	7585×	body	128	valid
403.0ms	887×	body	512	invalid
200.0ms	193×	body	2048	invalid
121.0ms	188×	body	1024	valid
95.0ms	322×	body	256	invalid
80.0ms	509×	body	128	invalid
54.0ms	131×	body	512	valid
24.0ms	83×	body	256	valid
13.0ms	13×	body	2048	valid

Compiler

Compiled 3138 to 1915 computations (39% saved)

Details

analyze2.0s (11.2%)

sample161.0ms (0.9%)

simplify64.0ms (0.4%)

prune8.0ms (0%)

localize21.0ms (0.1%)

rewrite103.0ms (0.6%)

series983.0ms (5.6%)

simplify90.0ms (0.5%)

prune199.0ms (1.1%)

localize40.0ms (0.2%)

rewrite316.0ms (1.8%)

series946.0ms (5.4%)

simplify111.0ms (0.6%)

prune600.0ms (3.4%)

localize32.0ms (0.2%)

rewrite194.0ms (1.1%)

series1.3s (7.4%)

simplify122.0ms (0.7%)

prune321.0ms (1.8%)

localize31.0ms (0.2%)

rewrite109.0ms (0.6%)

series609.0ms (3.5%)

simplify98.0ms (0.6%)

prune137.0ms (0.8%)

regimes1.6s (9.1%)

bsearch460.0ms (2.6%)

simplify7.0ms (0%)

end0.0ms (0%)

sample6.8s (39.2%)

Profiling