Details

analyze539.0ms (6%)

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 (0.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify259.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	5232	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

22.8b

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.im y.re) (.f64 x.re y.im))
22.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

22.7b

Rules

10×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
4×	`add-exp-log_binary64_1480` `add-log-exp_binary64_1481` `add-cbrt-cube_binary64_1478`
3×	`associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`pow1_binary64_1503` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `flip3-+_binary64_1445` `flip-+_binary64_1416` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1243 to 168 computations (86.5% saved)

series496.0ms (5.5%)

Error

4.0b

Counts

2 → 51

Calls

2 calls:

315.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
145.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1848 to 1169 computations (36.7% saved)

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	6080	2394

prune92.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Error

4.0b

Counts

96 → 7

Compiler

Compiled 1864 to 640 computations (65.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
13.2b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite170.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

43×	`*-un-lft-identity_binary64_1442`
28×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
10×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
8×	`associate-/r*_binary64_1386`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 96

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im 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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3624 to 1413 computations (61% saved)

series930.0ms (10.4%)

Error

4.0b

Counts

4 → 95

Calls

4 calls:

427.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
149.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
133.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
127.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 5996 to 3796 computations (36.7% saved)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5167	4985

prune229.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	191	7	198

Error

4.0b

Counts

198 → 7

Compiler

Compiled 5760 to 2326 computations (59.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
13.2b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite224.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

47×	`*-un-lft-identity_binary64_1442`
30×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
12×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
8×	`associate-/r*_binary64_1386`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 98

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im 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.re x.im) (.f64 y.im x.re))

Compiler

Compiled 3878 to 2286 computations (41.1% saved)

series971.0ms (10.8%)

Error

4.0b

Counts

4 → 95

Calls

4 calls:

438.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
154.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
133.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
126.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6438 to 4905 computations (23.8% saved)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5021	5015

prune317.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	193	7	200

Error

4.0b

Counts

200 → 7

Compiler

Compiled 6173 to 3699 computations (40.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b

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

0.5b

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

22.1b

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

rewrite268.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

138×	`times-frac_binary64_1448`
135×	`*-un-lft-identity_binary64_1442`
71×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464`
32×	`unpow-prod-down_binary64_1521` `distribute-lft-out_binary64_1393`
24×	`associate-/r*_binary64_1386`
16×	`add-exp-log_binary64_1480`
11×	`associate-/r/_binary64_1388`
10×	`add-cbrt-cube_binary64_1478`
8×	`div-exp_binary64_1493` `associate-/l*_binary64_1387`
6×	`div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417`
5×	`add-log-exp_binary64_1481`
4×	`pow1_binary64_1503` `cbrt-undiv_binary64_1476`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `associate-/l/_binary64_1389` `1-exp_binary64_1486` `rec-exp_binary64_1492`
1×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

3 → 159

Calls

3 calls:

16.0ms

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

13.0ms

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

4.0ms

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

Compiler

Compiled 5318 to 2577 computations (51.5% saved)

series823.0ms (9.2%)

Error

3.8b

Counts

3 → 81

Calls

3 calls:

311.0ms

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

279.0ms

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

162.0ms

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

Compiler

Compiled 4008 to 2985 computations (25.5% saved)

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5077	8831

prune258.0ms (2.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	236	4	240
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	237	10	247

Error

2.7b

Counts

247 → 10

Compiler

Compiled 5968 to 2795 computations (53.2% saved)

regimes1.1s (11.8%)

Accuracy

Total 11.9b remaining (80.8%)

Threshold costs 0b (0%)

Compiler

Compiled 6904 to 4328 computations (37.3% saved)

bsearch95.0ms (1.1%)

Steps

Iters	Range		Point
6	3.6194840668659824e+88	2.3704273472929405e+89	2.2891243310984562e+89
11	4.833211852758702e-137	1.6181936395343182e-112	9.294474795491087e-122
10	-2.4320586219243452e-67	-8.173962082196389e-86	-4.0222096243814814e-82
9	-2.779422430508317e+143	-3.766792668919958e+138	-1.438410299069282e+142

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	73	161
1	73	161

end0.0ms (0%)

sample1.7s (18.7%)

Algorithm

1×

intervals

Results

348.0ms	8000×	body	128	valid
27.0ms	478×	body	128	invalid

Compiler

Compiled 1437 to 887 computations (38.3% saved)

Details

analyze539.0ms (6%)

sample24.0ms (0.3%)

simplify259.0ms (2.9%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite70.0ms (0.8%)

series496.0ms (5.5%)

simplify84.0ms (0.9%)

prune92.0ms (1%)

localize17.0ms (0.2%)

rewrite170.0ms (1.9%)

series930.0ms (10.4%)

simplify95.0ms (1.1%)

prune229.0ms (2.6%)

localize15.0ms (0.2%)

rewrite224.0ms (2.5%)

series971.0ms (10.8%)

simplify95.0ms (1.1%)

prune317.0ms (3.5%)

localize12.0ms (0.1%)

rewrite268.0ms (3%)

series823.0ms (9.2%)

simplify131.0ms (1.5%)

prune258.0ms (2.9%)

regimes1.1s (11.8%)

bsearch95.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.7s (18.7%)

Profiling