Details

analyze804.0ms (11.5%)

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)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
2.0ms	50×	body	128	invalid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify116.0ms (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

prune4.0ms (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

4.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	13.7b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

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)
✓	4.8b	(/.f64 y (fma.f64 z z z))
✓	6.4b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

rewrite32.0ms (0.5%)

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))
4.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms	(/.f64 y (fma.f64 z z z))

series206.0ms (2.9%)

Counts

3 → 84

Calls

3 calls:

118.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
53.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
35.0ms	(/.f64 y (fma.f64 z z z))

simplify196.0ms (2.8%)

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 → 433

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

prune281.0ms (4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	422	11	433
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	423	12	435

Error

1.0b

Counts

435 → 12

Alt Table

Status	Error	Program
	4.5b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
	53.1b	(.f64 (.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))) (*.f64 (sqrt.f64 x) (/.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z))))
	14.0b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	11.6b	(.f64 x (/.f64 y (.f64 z (fma.f64 z z z))))
	20.7b	(*.f64 x (/.f64 (/.f64 y z) z))
	19.5b	(.f64 x (/.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 y (fma.f64 z z z)) (/.f64 y (fma.f64 z z z))) (/.f64 y (fma.f64 z z z)))) z))
	4.2b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
	14.1b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	26.5b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
▶	4.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	6.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	34.9b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))

Compiler

Compiled 6328 to 1465 computations (76.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	4.8b	(/.f64 y (fma.f64 z z z))
✓	4.9b	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite12.0ms (0.2%)

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

series196.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

111.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
85.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

simplify95.0ms (1.4%)

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 → 246

Iterations

Useful iterations: 2 (0.0ms)

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

prune173.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	328	4	332
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	333	11	344

Error

0.7b

Counts

344 → 11

Alt Table

Status	Error	Program
	14.0b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	11.6b	(.f64 x (/.f64 y (.f64 z (fma.f64 z z z))))
	42.6b	(/.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) (fma.f64 z z z)) z)
▶	4.2b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
✓	4.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	4.5b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
✓	6.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	34.9b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	32.5b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	4.2b	(/.f64 (*.f64 x (/.f64 1 (/.f64 (fma.f64 z z z) y))) z)

Compiler

Compiled 3307 to 956 computations (71.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.4b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
	4.8b	(/.f64 y (fma.f64 z z z))
	4.9b	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
20×	`prod-exp_binary64`
13×	`associate-r_binary64`
10×	`cbrt-unprod_binary64`

Counts

1 → 48

Calls

1 calls:

7.0ms

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

series104.0ms (1.5%)

Counts

1 → 36

Calls

1 calls:

104.0ms

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

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

798×	`times-frac_binary64`
611×	`associate-*l/_binary64`
545×	`fma-def_binary64`
504×	`associate-/l*_binary64`
299×	`fma-neg_binary64`

Counts

84 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1588
1	310	1380
2	1083	1336
3	4465	1336
4	4967	1336

prune194.0ms (2.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	461	2	463
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	464	10	474

Error

0.7b

Counts

474 → 10

Alt Table

Status	Error	Program
	34.9b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	8.6b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
	14.0b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	11.6b	(.f64 x (/.f64 y (.f64 z (fma.f64 z z z))))
	42.6b	(/.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) (fma.f64 z z z)) (/.f64 1 z))
✓	4.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
▶	4.5b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
✓	6.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	32.5b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)

Compiler

Compiled 4098 to 1430 computations (65.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(cbrt.f64 y)
✓	0.9b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
✓	1.8b	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
✓	3.4b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))

rewrite66.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

260×	`times-frac_binary64`
148×	`add-sqr-sqrt_binary64`
145×	`*-un-lft-identity_binary64`
145×	`add-cube-cbrt_binary64`
141×	`associate-r_binary64`

Counts

4 → 274

Calls

4 calls:

29.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
12.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
3.0ms	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
1.0ms	(cbrt.f64 y)

series1.9s (27.2%)

Counts

4 → 108

Calls

4 calls:

1.2s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
306.0ms	(/.f64 (cbrt.f64 y) (fma.f64 z z z))
251.0ms	(cbrt.f64 y)
137.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))

simplify216.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

597×	`associate-*l/_binary64`
571×	`associate-*r/_binary64`
505×	`associate-/l*_binary64`
322×	`times-frac_binary64`
258×	`associate-/r*_binary64`

Counts

382 → 716

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	13132
1	1462	9773
2	5215	9773

prune388.0ms (5.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	716	0	716
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	716	10	726

Error

0.7b

Counts

726 → 10

Alt Table

Status	Error	Program
	34.9b	(.f64 x (/.f64 (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z)))) z))
	8.6b	(/.f64 (/.f64 (*.f64 y x) z) (fma.f64 z z z))
	14.0b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	11.6b	(.f64 x (/.f64 y (.f64 z (fma.f64 z z z))))
	42.6b	(/.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) (fma.f64 z z z)) (/.f64 1 z))
✓	4.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	4.5b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (fma.f64 z z z)) (cbrt.f64 z)))
✓	6.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	32.5b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)

Compiler

Compiled 16697 to 2896 computations (82.7% saved)

regimes937.0ms (13.4%)

Accuracy

Total 2.2b remaining (65.7%)

Threshold costs 0b (0%)

Compiler

Compiled 14649 to 7840 computations (46.5% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	109
1	41	109
2	40	109

end8.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 225 to 99 computations (56% saved)

sample882.0ms (12.6%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
69.0ms	1518×	body	128	invalid

Compiler

Compiled 273 to 141 computations (48.4% saved)

Details

analyze804.0ms (11.5%)

sample31.0ms (0.4%)

simplify116.0ms (1.7%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite32.0ms (0.5%)

series206.0ms (2.9%)

simplify196.0ms (2.8%)

prune281.0ms (4%)

localize6.0ms (0.1%)

rewrite12.0ms (0.2%)

series196.0ms (2.8%)

simplify95.0ms (1.4%)

prune173.0ms (2.5%)

localize7.0ms (0.1%)

rewrite10.0ms (0.1%)

series104.0ms (1.5%)

simplify103.0ms (1.5%)

prune194.0ms (2.8%)

localize14.0ms (0.2%)

rewrite66.0ms (0.9%)

series1.9s (27.2%)

simplify216.0ms (3.1%)

prune388.0ms (5.5%)

regimes937.0ms (13.4%)

bsearch9.0ms (0.1%)

simplify5.0ms (0.1%)

end8.0ms (0.1%)

sample882.0ms (12.6%)

Profiling