Details

analyze649.0ms (6.1%)

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
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample24.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify102.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (0%)

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

23.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.0b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite97.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

23.3b

Rules

10×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
9×	`times-frac_binary64_1107`
4×	`add-exp-log_binary64_1139` `add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`pow1_binary64_1162` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

2 → 42

Calls

2 calls:

12.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 1203 to 160 computations (86.7% saved)

series584.0ms (5.5%)

Error

4.8b

Counts

2 → 48

Calls

2 calls:

369.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
168.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

Compiler

Compiled 1644 to 1011 computations (38.5% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5131	2283

prune104.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Error

4.7b

Counts

91 → 8

Compiler

Compiled 1862 to 672 computations (63.9% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
14.5b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite240.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

47×	`*-un-lft-identity_binary64_1101`
30×	`sqrt-prod_binary64_1117`
25×	`add-sqr-sqrt_binary64_1123`
24×	`times-frac_binary64_1107`
23×	`add-cube-cbrt_binary64_1136`
12×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
8×	`associate-/r*_binary64_1045`
6×	`pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
3×	`associate-/l*_binary64_1046`
2×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))

Compiler

Compiled 3813 to 2242 computations (41.2% saved)

series1.2s (11.3%)

Error

4.7b

Counts

4 → 93

Calls

4 calls:

491.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
207.0ms	(+.f64 (.f64 y.im x.im) (.f64 y.re x.re))
186.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
165.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6318 to 4802 computations (24% saved)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5029	4836

prune355.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	189	8	197

Error

4.7b

Counts

197 → 8

Compiler

Compiled 6084 to 3652 computations (40% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b

(+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))

0.7b

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))))

22.4b

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re)))

rewrite333.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

138×	`times-frac_binary64_1107`
135×	`*-un-lft-identity_binary64_1101`
71×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123`
32×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
24×	`associate-/r*_binary64_1045`
16×	`add-exp-log_binary64_1139`
11×	`associate-/r/_binary64_1047`
10×	`add-cbrt-cube_binary64_1137`
8×	`div-exp_binary64_1152` `associate-/l*_binary64_1046`
7×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`div-inv_binary64_1098`
5×	`add-log-exp_binary64_1140`
4×	`pow1_binary64_1162` `cbrt-undiv_binary64_1135`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `1-exp_binary64_1145` `rec-exp_binary64_1151`
1×	`inv-pow_binary64_1186` `pow-flip_binary64_1175` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

3 → 158

Calls

3 calls:

19.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re)))

16.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))))

4.0ms

(+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))

Compiler

Compiled 5299 to 2565 computations (51.6% saved)

series949.0ms (8.9%)

Error

4.7b

Counts

3 → 78

Calls

3 calls:

376.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re)))

336.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))))

166.0ms

(+.f64 (*.f64 y.im x.im) (*.f64 y.re x.re))

Compiler

Compiled 3756 to 2784 computations (25.9% saved)

simplify135.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5120	8728

prune325.0ms (3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	232	4	236
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	234	10	244

Error

2.7b

Counts

244 → 10

Compiler

Compiled 6048 to 2918 computations (51.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

14.5b	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite304.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

30×	`sqrt-div_binary64_1118`
21×	`*-un-lft-identity_binary64_1101`
15×	`sqrt-prod_binary64_1117`
12×	`add-sqr-sqrt_binary64_1123`
10×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136`
8×	`associate-/r/_binary64_1047`
7×	`pow1_binary64_1162`
6×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
4×	`add-log-exp_binary64_1140` `frac-times_binary64_1111`
3×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `times-frac_binary64_1107` `associate-/l*_binary64_1046`
2×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/l/_binary64_1048` `associate-l/_binary64_1044` `associate-r/_binary64_1043`
1×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/r*_binary64_1045`

Counts

4 → 82

Calls

4 calls:

35.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 4247 to 2867 computations (32.5% saved)

series1.3s (11.7%)

Error

2.7b

Counts

4 → 87

Calls

4 calls:

523.0ms	(/.f64 (+.f64 (.f64 y.im x.im) (.f64 y.re x.re)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
194.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
183.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
181.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 7512 to 5715 computations (23.9% saved)

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4981	3917
1	4981	3917

prune451.0ms (4.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	169	10	179

Error

2.7b

Counts

179 → 10

Compiler

Compiled 6558 to 4279 computations (34.8% saved)

regimes1.1s (10.6%)

Accuracy

Total 11.9b remaining (82.4%)

Threshold costs 0b (0%)

Compiler

Compiled 7196 to 4576 computations (36.4% saved)

bsearch118.0ms (1.1%)

Steps

Iters	Range		Point
8	1.978134698787934e+41	6.464176775332817e+45	4.621378501818419e+44
8	2.593154302110071e-147	1.632803671243665e-142	1.1429473994431096e-145
9	-2.271203142594088e-161	-8.203157505463325e-167	-1.005001047695393e-161
9	-5.810018931600796e+144	-2.000326219039384e+136	-3.6836303645104744e+137

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	53	175
1	53	175

end0.0ms (0%)

sample2.0s (18.7%)

Algorithm

1×

intervals

Results

393.0ms	8000×	body	128	valid
27.0ms	463×	body	128	invalid

Compiler

Compiled 1502 to 954 computations (36.5% saved)

Details

analyze649.0ms (6.1%)

sample24.0ms (0.2%)

simplify102.0ms (1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite97.0ms (0.9%)

series584.0ms (5.5%)

simplify65.0ms (0.6%)

prune104.0ms (1%)

localize22.0ms (0.2%)

rewrite240.0ms (2.2%)

series1.2s (11.3%)

simplify101.0ms (0.9%)

prune355.0ms (3.3%)

localize14.0ms (0.1%)

rewrite333.0ms (3.1%)

series949.0ms (8.9%)

simplify135.0ms (1.3%)

prune325.0ms (3%)

localize18.0ms (0.2%)

rewrite304.0ms (2.8%)

series1.3s (11.7%)

simplify97.0ms (0.9%)

prune451.0ms (4.2%)

regimes1.1s (10.6%)

bsearch118.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.0s (18.7%)

Profiling