Details

analyze872.0ms (16.1%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
2.0ms	53×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-*r/_binary64`
769×	`associate-/l/_binary64`
660×	`associate-*l/_binary64`
522×	`associate-/l*_binary64`
421×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	30	16
2	78	14
3	195	14
4	314	14
5	383	14
6	426	14
7	631	14
8	1009	14
9	2204	14
10	2868	14
11	2967	14
12	3079	14
13	3193	14
14	3058	14
15	3712	14
16	4988	14
17	4824	14

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

5.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	13.1b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
▶	10.2b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y (fma.f64 z z z)) z)
✓	5.0b	(/.f64 y (fma.f64 z z z))
✓	9.7b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series215.0ms (4%)

Counts

3 → 84

Calls

3 calls:

124.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
56.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
34.0ms	(/.f64 y (fma.f64 z z z))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

3 → 168

Calls

3 calls:

11.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
6.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms	(/.f64 y (fma.f64 z z z))

simplify175.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
353×	`fma-neg_binary64`
351×	`*-commutative_binary64`
341×	`associate-/r/_binary64`
275×	`sub-neg_binary64`

Counts

252 → 296

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	4846
1	687	4599
2	2304	4515
3	3607	4509
4	4817	4509
5	4963	4509

prune316.0ms (5.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	287	9	296
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	288	10	298

Error

1.4b

Counts

298 → 10

Alt Table

Status	Error	Program
	14.4b	(.f64 x (.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
	27.3b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	10.2b	(*.f64 x (/.f64 (/.f64 1 (/.f64 (fma.f64 z z z) y)) z))
▶	4.6b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	33.3b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (sqrt.f64 z))) (/.f64 (/.f64 y (cbrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
	10.7b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	25.7b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	22.1b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
	10.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 (/.f64 y (fma.f64 z z z)) z)))
✓	10.2b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

Compiler

Compiled 6277 to 1442 computations (77% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	5.0b	(/.f64 y (fma.f64 z z z))
✓	5.3b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series174.0ms (3.2%)

Counts

2 → 72

Calls

2 calls:

103.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
71.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))
5.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-neg_binary64`
483×	`associate-l_binary64`
433×	`associate-/r*_binary64`
417×	`associate-r_binary64`
378×	`associate-/r/_binary64`

Counts

132 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2289
1	397	2096
2	1539	1990
3	4439	1990
4	4968	1990

prune175.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	175	10	185

Error

0.5b

Counts

185 → 10

Alt Table

Status	Error	Program
	9.7b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	11.7b	(/.f64 (.f64 (.f64 x (/.f64 1 (sqrt.f64 (fma.f64 z z z)))) (/.f64 y (sqrt.f64 (fma.f64 z z z)))) z)
	14.4b	(.f64 x (.f64 y (/.f64 1 (*.f64 z (fma.f64 z z z)))))
	27.3b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	25.7b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
▶	4.8b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
	22.1b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
	41.7b	(/.f64 (.f64 x (.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
	32.0b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	10.7b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (fma.f64 z z z))) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))

Compiler

Compiled 3326 to 955 computations (71.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
✓	0.6b	(/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z))))
	5.0b	(/.f64 y (fma.f64 z z z))
	5.3b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series142.0ms (2.6%)

Counts

2 → 72

Calls

2 calls:

101.0ms	(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
41.0ms	(/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
39×	`times-frac_binary64`
25×	`add-cbrt-cube_binary64`
24×	`div-exp_binary64`
21×	`*-un-lft-identity_binary64`

Counts

2 → 92

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
4.0ms	(/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z))))

simplify116.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

661×	`associate-*l/_binary64`
661×	`associate-/r/_binary64`
550×	`associate-/l/_binary64`
449×	`fma-def_binary64`
134×	`fma-neg_binary64`

Counts

164 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	3455
1	339	3061
2	1348	2694
3	4340	2694
4	4967	2694

prune257.0ms (4.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	269	11	280

Error

0.5b

Counts

280 → 11

Alt Table

Status	Error	Program
	32.1b	(/.f64 1 (/.f64 z (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))))))
	9.7b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	11.7b	(/.f64 (.f64 (.f64 x (/.f64 1 (sqrt.f64 (fma.f64 z z z)))) (/.f64 y (sqrt.f64 (fma.f64 z z z)))) z)
	25.7b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	27.3b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
✓	4.8b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
	22.1b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
▶	4.9b	(/.f64 1 (.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z))))))
	41.7b	(/.f64 (.f64 x (.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
	8.6b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
	32.0b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)

Compiler

Compiled 5462 to 1745 computations (68.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z))))))
✓	0.6b	(.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z)))))
	5.0b	(/.f64 y (fma.f64 z z z))
	5.3b	(*.f64 x (/.f64 y (fma.f64 z z z)))

series149.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

109.0ms	(/.f64 1 (.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z))))))
40.0ms	(.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z)))))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`add-exp-log_binary64`
64×	`prod-exp_binary64`
58×	`div-exp_binary64`
36×	`add-cbrt-cube_binary64`
23×	`rec-exp_binary64`

Counts

2 → 101

Calls

2 calls:

9.0ms	(/.f64 1 (.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z))))))
8.0ms	(.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z)))))

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

636×	`associate-/r*_binary64`
602×	`associate-/l*_binary64`
478×	`associate-/r/_binary64`
432×	`fma-def_binary64`
319×	`associate-/l/_binary64`

Counts

173 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	3412
1	355	2939
2	1270	2583
3	4600	2583
4	5103	2583

prune227.0ms (4.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	268	11	279

Error

0.5b

Counts

279 → 11

Alt Table

Status	Error	Program
	32.1b	(/.f64 1 (/.f64 z (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))))))
	9.7b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	11.7b	(/.f64 (.f64 (.f64 x (/.f64 1 (sqrt.f64 (fma.f64 z z z)))) (/.f64 y (sqrt.f64 (fma.f64 z z z)))) z)
	25.7b	(.f64 (.f64 x (sqrt.f64 y)) (/.f64 (/.f64 (sqrt.f64 y) (fma.f64 z z z)) z))
	27.3b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
✓	4.8b	(/.f64 1 (/.f64 z (*.f64 x (/.f64 y (fma.f64 z z z)))))
	22.1b	(/.f64 (*.f64 y x) (+.f64 (pow.f64 z 2) (pow.f64 z 3)))
✓	4.9b	(/.f64 1 (.f64 z (/.f64 1 (.f64 x (/.f64 y (fma.f64 z z z))))))
	41.7b	(/.f64 (.f64 x (.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
	8.6b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
	32.0b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)

Compiler

Compiled 5570 to 2143 computations (61.5% saved)

regimes954.0ms (17.6%)

Accuracy

Total 2.9b remaining (72.5%)

Threshold costs 0b (0%)

Counts

162 → 1

Compiler

Compiled 18610 to 10115 computations (45.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	46
1	16	46
2	16	46

end6.0ms (0.1%)

Compiler: Compiled 99 to 39 computations (60.6% saved)

sample1.2s (21.9%)

Algorithm

1×

intervals

Results

412.0ms	8000×	body	128	valid
63.0ms	1514×	body	128	invalid

Compiler

Compiled 238 to 131 computations (45% saved)

Details

analyze872.0ms (16.1%)

sample34.0ms (0.6%)

simplify93.0ms (1.7%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series215.0ms (4%)

rewrite35.0ms (0.6%)

simplify175.0ms (3.2%)

prune316.0ms (5.8%)

localize7.0ms (0.1%)

series174.0ms (3.2%)

rewrite14.0ms (0.3%)

simplify99.0ms (1.8%)

prune175.0ms (3.2%)

localize8.0ms (0.1%)

series142.0ms (2.6%)

rewrite18.0ms (0.3%)

simplify116.0ms (2.1%)

prune257.0ms (4.7%)

localize9.0ms (0.2%)

series149.0ms (2.8%)

rewrite28.0ms (0.5%)

simplify100.0ms (1.8%)

prune227.0ms (4.2%)

regimes954.0ms (17.6%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample1.2s (21.9%)

Profiling