Details

analyze310.0ms (6.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample34.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
7×	`associate-r_binary64`
7×	`associate-l_binary64`
5×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	24	8
3	47	8
4	43	8
5	45	8
6	43	8

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

4.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.4b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize45.0ms (0.9%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.1b	(*.f64 x (fma.f64 y y 1))

series25.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

25.0ms

(*.f64 x (fma.f64 y y 1))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

6.0ms

(*.f64 x (fma.f64 y y 1))

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

746×	`unswap-sqr_binary64`
561×	`distribute-rgt-in_binary64`
550×	`fma-def_binary64`
534×	`distribute-lft-in_binary64`
336×	`distribute-rgt-out_binary64`

Counts

46 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	447
1	81	404
2	264	404
3	597	404
4	1918	404
5	2078	404
6	2869	404
7	4919	404
8	4929	404

prune64.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Error

1.7b

Counts

41 → 8

Alt Table

Status	Error	Program
✓	4.4b	(*.f64 x (fma.f64 y y 1))
	4.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	5.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (fma.f64 y y 1)))
	26.7b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))
	45.3b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (*.f64 (fma.f64 y y 1) (fma.f64 y y 1)) (fma.f64 y y 1))))
	41.8b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
	20.3b	x
▶	4.4b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))

Compiler

Compiled 633 to 374 computations (40.9% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 y)
✓	0.0b	(*.f64 x (hypot.f64 1 y))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
✓	4.0b	(sqrt.f64 (fma.f64 y y 1))

series114.0ms (2.4%)

Counts

4 → 72

Calls

4 calls:

66.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
32.0ms	(*.f64 x (hypot.f64 1 y))
10.0ms	(hypot.f64 1 y)
5.0ms	(sqrt.f64 (fma.f64 y y 1))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`associate-r_binary64`

Counts

4 → 68

Calls

4 calls:

9.0ms	(.f64 (.f64 x (hypot.f64 1 y)) (sqrt.f64 (fma.f64 y y 1)))
5.0ms	(*.f64 x (hypot.f64 1 y))
2.0ms	(sqrt.f64 (fma.f64 y y 1))
1.0ms	(hypot.f64 1 y)

simplify161.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

897×	`fma-neg_binary64`
400×	`times-frac_binary64`
387×	`fma-def_binary64`
312×	`cancel-sign-sub-inv_binary64`
293×	`associate-*l/_binary64`

Counts

140 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1769
1	362	1393
2	1008	1363
3	2521	1354
4	4802	1354
5	5209	1354

prune231.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	136	8	144

Error

0.0b

Counts

144 → 8

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))
	41.8b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
✓	4.4b	(*.f64 x (fma.f64 y y 1))
	4.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
	26.7b	(.f64 (.f64 (sqrt.f64 x) (hypot.f64 1 y)) (*.f64 (sqrt.f64 x) (hypot.f64 1 y)))
	39.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 x (hypot.f64 1 y)) 3)) (sqrt.f64 (fma.f64 y y 1)))
	4.5b	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (sqrt.f64 (fma.f64 y y 1))))
	0.2b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 (sqrt.f64 (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))))

Compiler

Compiled 2451 to 1654 computations (32.5% saved)

localize16.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 y)
	0.0b	(*.f64 x (hypot.f64 1 y))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))

series99.0ms (2.1%)

Counts

1 → 24

Calls

1 calls:

99.0ms

(*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
13×	`prod-exp_binary64`
13×	`pow1_binary64`
8×	`cbrt-unprod_binary64`

Counts

1 → 26

Calls

1 calls:

15.0ms

(*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))

simplify169.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

574×	`log-div_binary64`
450×	`times-frac_binary64`
443×	`associate-/l/_binary64`
415×	`associate-/r/_binary64`
340×	`associate-l_binary64`

Counts

50 → 38

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	694
1	107	552
2	297	523
3	439	523
4	582	484
5	806	484
6	1400	484
7	3361	484
8	4788	484
9	5183	484

prune196.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Error

0.0b

Counts

102 → 7

Alt Table

Status	Error	Program
	35.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 x (hypot.f64 1 y)) 3)) (*.f64 1 (hypot.f64 1 y)))
	4.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))
	41.8b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
✓	4.4b	(*.f64 x (fma.f64 y y 1))
	4.5b	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (sqrt.f64 (fma.f64 y y 1))))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y))))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))

Compiler

Compiled 1801 to 1295 computations (28.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y))))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))
✓	0.6b	(cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y))))

series1.5s (30.3%)

Counts

3 → 72

Calls

3 calls:

765.0ms

(cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y))))

649.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))

41.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y))))) (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y))))) (cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))

4.0ms

(cbrt.f64 (*.f64 (*.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y))))

simplify163.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

517×	`fma-def_binary64`
492×	`fma-neg_binary64`
307×	`*-commutative_binary64`
197×	`exp-prod_binary64`
190×	`sub-neg_binary64`

Counts

151 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	3775
1	534	3373
2	1459	2760
3	3818	2174
4	5000	2174
5	5001	2174

prune460.0ms (9.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	380	0	380
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	380	7	387

Error

0.0b

Counts

387 → 7

Alt Table

Status	Error	Program
	35.6b	(.f64 (cbrt.f64 (pow.f64 (.f64 x (hypot.f64 1 y)) 3)) (*.f64 1 (hypot.f64 1 y)))
	4.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (fma.f64 y y 1)) (cbrt.f64 (fma.f64 y y 1)))) (cbrt.f64 (fma.f64 y y 1)))
✓	0.1b	(.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))
	41.8b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 y y 1) x) 3))
✓	4.4b	(*.f64 x (fma.f64 y y 1))
	4.5b	(.f64 (.f64 (*.f64 x (hypot.f64 1 y)) (sqrt.f64 (hypot.f64 1 y))) (sqrt.f64 (sqrt.f64 (fma.f64 y y 1))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y)))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (.f64 1 (hypot.f64 1 y))))) (cbrt.f64 (.f64 (.f64 x (hypot.f64 1 y)) (*.f64 1 (hypot.f64 1 y)))))

Compiler

Compiled 16288 to 12256 computations (24.8% saved)

regimes346.0ms (7.2%)

Accuracy

Total 0.1b remaining (73.1%)

Threshold costs 0.1b (73.1%)

Counts

54 → 1

Compiler

Compiled 5176 to 3786 computations (26.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	11	13
2	10	13

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample658.0ms (13.7%)

Algorithm

1×

intervals

Results

271.0ms	8000×	body	128	valid
12.0ms	176×	body	128	invalid

Compiler

Compiled 151 to 112 computations (25.8% saved)

Details

analyze310.0ms (6.4%)

sample34.0ms (0.7%)

simplify15.0ms (0.3%)

prune5.0ms (0.1%)

localize45.0ms (0.9%)

series25.0ms (0.5%)

rewrite8.0ms (0.2%)

simplify112.0ms (2.3%)

prune64.0ms (1.3%)

localize22.0ms (0.5%)

series114.0ms (2.4%)

rewrite28.0ms (0.6%)

simplify161.0ms (3.4%)

prune231.0ms (4.8%)

localize16.0ms (0.3%)

series99.0ms (2.1%)

rewrite19.0ms (0.4%)

simplify169.0ms (3.5%)

prune196.0ms (4.1%)

localize19.0ms (0.4%)

series1.5s (30.3%)

rewrite27.0ms (0.6%)

simplify163.0ms (3.4%)

prune460.0ms (9.6%)

regimes346.0ms (7.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample658.0ms (13.7%)

Profiling