Details

analyze566.0ms (15%)

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 8 to 8 computations (0% saved)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
1.0ms	44×	body	128	invalid

Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify103.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	160	14
1	160	14

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

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_1822`
1×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `*-un-lft-identity_binary64_1783` `flip--_binary64_1758` `sub-neg_binary64_1776` `pow1_binary64_1844`

Counts

1 → 12

Calls

1 calls:

4.0ms

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

series45.0ms (1.2%)

Counts

1 → 3

Calls

1 calls:

45.0ms

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

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4948	294
1	4948	294

prune12.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Error

0.0b

Counts

16 → 3

Compiler

Compiled 226 to 59 computations (73.9% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
1.7b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.7b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.7b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1814`
23×	`add-sqr-sqrt_binary64_1805`
18×	`cbrt-div_binary64_1815`
15×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
11×	`pow1_binary64_1844`
9×	`flip3--_binary64_1787` `pow1/3_binary64_1865` `flip--_binary64_1758`
6×	`swap-sqr_binary64_1750` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `associate-r_binary64_1723`
4×	`add-cbrt-cube_binary64_1819` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
2×	`associate-r/_binary64_1725` `pow-prod-up_binary64_1853` `associate-l/_binary64_1726` `pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-plus_binary64_1846` `*-commutative_binary64_1714` `pow2_binary64_1864`

Counts

4 → 87

Calls

4 calls:

12.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
3.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
3.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series632.0ms (16.7%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
156.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
145.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
139.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

simplify84.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4949	2776
1	4949	2776

prune95.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Error

0.0b

Counts

102 → 4

Compiler

Compiled 3270 to 561 computations (82.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.3b	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
1.1b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.1b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_1805`
24×	`sqrt-prod_binary64_1799`
21×	`pow1_binary64_1844`
16×	`sqrt-div_binary64_1800`
14×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801`
9×	`flip3--_binary64_1787` `flip--_binary64_1758`
8×	`swap-sqr_binary64_1750`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `associate-l_binary64_1724` `add-log-exp_binary64_1822` `associate-r_binary64_1723`
5×	`pow-prod-up_binary64_1853`
4×	`frac-times_binary64_1793` `unswap-sqr_binary64_1751` `rem-sqrt-square_binary64_1796`
3×	`pow-sqr_binary64_1756` `pow-prod-down_binary64_1854`
2×	`associate-r/_binary64_1725` `associate-l/_binary64_1726`
1×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `sqrt-unprod_binary64_1803` `pow-plus_binary64_1846` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `*-commutative_binary64_1714` `rem-square-sqrt_binary64_1795` `sub-neg_binary64_1776` `sqr-abs_binary64_1798` `pow2_binary64_1864`

Counts

4 → 100

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series273.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
88.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
44.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
44.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify63.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4953	2577
1	4953	2577

prune79.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	113	3	116

Error

0.0b

Counts

116 → 3

Compiler

Compiled 2353 to 431 computations (81.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))) 3))
0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) 3)
1.1b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.1b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite54.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`sqrt-prod_binary64_1799`
70×	`add-sqr-sqrt_binary64_1805`
32×	`sqrt-div_binary64_1800`
27×	`unpow-prod-down_binary64_1862` `cube-prod_binary64_1811`
24×	`unswap-sqr_binary64_1751` `associate-r_binary64_1723`
23×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`add-exp-log_binary64_1821` `pow1_binary64_1844`
9×	`flip3--_binary64_1787` `associate-l_binary64_1724` `flip--_binary64_1758`
8×	`cube-div_binary64_1812`
7×	`add-cbrt-cube_binary64_1819`
6×	`sqrt-pow1_binary64_1801`
5×	`sqr-pow_binary64_1755` `pow-pow_binary64_1855`
4×	`pow1/2_binary64_1863` `frac-times_binary64_1793` `add-log-exp_binary64_1822`
3×	`prod-exp_binary64_1832` `pow-unpow_binary64_1860`
2×	`associate-r/_binary64_1725` `cube-mult_binary64_1813` `unpow3_binary64_1849` `associate-l/_binary64_1726` `rem-sqrt-square_binary64_1796` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`rem-cube-cbrt_binary64_1806` `cbrt-unprod_binary64_1816` `pow-prod-up_binary64_1853` `*-commutative_binary64_1714` `sqrt-pow2_binary64_1802`

Counts

4 → 150

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))) 3))
7.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) 3)
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series585.0ms (15.5%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) 3)
94.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
87.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
51.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))) 3))

simplify93.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5047	4550

prune135.0ms (3.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	162	3	165

Error

0.0b

Counts

165 → 3

Compiler

Compiled 4150 to 856 computations (79.4% saved)

regimes125.0ms (3.3%)

Accuracy

Total 0.0b remaining (43%)

Threshold costs 0.0b (43%)

Compiler

Compiled 1154 to 682 computations (40.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

end0.0ms (0%)

sample639.0ms (16.9%)

Algorithm

1×

intervals

Results

209.0ms	8000×	body	128	valid
35.0ms	1448×	body	128	invalid

Compiler

Compiled 175 to 107 computations (38.9% saved)

Details

analyze566.0ms (15%)

sample17.0ms (0.4%)

simplify103.0ms (2.7%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite4.0ms (0.1%)

series45.0ms (1.2%)

simplify68.0ms (1.8%)

prune12.0ms (0.3%)

localize12.0ms (0.3%)

rewrite32.0ms (0.8%)

series632.0ms (16.7%)

simplify84.0ms (2.2%)

prune95.0ms (2.5%)

localize8.0ms (0.2%)

rewrite32.0ms (0.9%)

series273.0ms (7.2%)

simplify63.0ms (1.7%)

prune79.0ms (2.1%)

localize10.0ms (0.3%)

rewrite54.0ms (1.4%)

series585.0ms (15.5%)

simplify93.0ms (2.5%)

prune135.0ms (3.6%)

regimes125.0ms (3.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample639.0ms (16.9%)

Profiling