Details

analyze734.0ms (7.5%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample54.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify32.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

prune9.0ms (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

7.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.8b	(*.f64 y (fma.f64 z z 1))
✓	4.3b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

15.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
6.0ms	(*.f64 y (fma.f64 z z 1))

series284.0ms (2.9%)

Counts

2 → 60

Calls

2 calls:

230.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
53.0ms	(*.f64 y (fma.f64 z z 1))

simplify273.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64`
453×	`associate-l_binary64`
414×	`associate-/l*_binary64`
336×	`associate-/l/_binary64`
297×	`associate-r_binary64`

Counts

134 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2203
1	330	1967
2	1107	1965
3	3956	1963
4	4482	1963
5	4806	1963
6	4938	1963

prune244.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	248	8	256
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	8	257

Error

4.0b

Counts

257 → 8

Alt Table

Status	Error	Program
	7.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	7.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (.f64 y (fma.f64 z z 1)) (/.f64 1 (cbrt.f64 x))))
	30.2b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 y (.f64 z z) y) x) 3)))
	50.3b	(/.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (*.f64 y (fma.f64 z z 1)) (sqrt.f64 (/.f64 1 x))))
▶	7.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
	7.6b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	24.3b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	7.4b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))

Compiler

Compiled 2484 to 1426 computations (42.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (hypot.f64 1 z))
✓	0.1b	(.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
✓	4.3b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
✓	13.3b	(sqrt.f64 (fma.f64 z z 1))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
31×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`

Counts

4 → 116

Calls

4 calls:

15.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
12.0ms	(.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
5.0ms	(*.f64 y (hypot.f64 1 z))
2.0ms	(sqrt.f64 (fma.f64 z z 1))

series679.0ms (7%)

Counts

4 → 96

Calls

4 calls:

449.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
150.0ms	(.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
69.0ms	(*.f64 y (hypot.f64 1 z))
11.0ms	(sqrt.f64 (fma.f64 z z 1))

simplify270.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/l*_binary64`
472×	`associate-/l/_binary64`
412×	`fma-def_binary64`
240×	`associate-l_binary64`
198×	`associate-/r*_binary64`

Counts

212 → 400

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	4001
1	619	2902
2	1916	2883
3	4768	2883
4	4984	2883
5	4965	2883

prune537.0ms (5.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	392	8	400
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	399	9	408

Error

0.0b

Counts

408 → 9

Alt Table

Status	Error	Program
	49.0b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (.f64 y (hypot.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))
	30.2b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 y (.f64 z z) y) x) 3)))
	7.0b	(/.f64 (/.f64 1 x) (pow.f64 (*.f64 y (fma.f64 z z 1)) 1))
	2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))
▶	1.8b	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
	2.1b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	7.3b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
	4.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (*.f64 1 (hypot.f64 1 z))))
	7.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))

Compiler

Compiled 5211 to 3486 computations (33.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (hypot.f64 1 z))
✓	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	0.5b	(/.f64 1 (*.f64 y (hypot.f64 1 z)))
✓	1.8b	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))

rewrite84.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`add-exp-log_binary64`
152×	`times-frac_binary64`
96×	`add-sqr-sqrt_binary64`
85×	`*-un-lft-identity_binary64`
84×	`add-cube-cbrt_binary64`

Counts

3 → 216

Calls

3 calls:

34.0ms	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
9.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
8.0ms	(/.f64 1 (*.f64 y (hypot.f64 1 z)))

series654.0ms (6.7%)

Counts

3 → 84

Calls

3 calls:

293.0ms	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
240.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
120.0ms	(/.f64 1 (*.f64 y (hypot.f64 1 z)))

simplify474.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
382×	`*-commutative_binary64`
364×	`sub-neg_binary64`
332×	`associate-/r/_binary64`
280×	`fma-neg_binary64`

Counts

300 → 553

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	309	6585
1	799	5822
2	2440	5764
3	3810	5760
4	4905	5760
5	4979	5760
6	4942	5760

prune932.0ms (9.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	626	4	630
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	630	9	639

Error

Counts

639 → 9

Alt Table

Status	Error	Program
	49.0b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (.f64 y (hypot.f64 1 z))) (/.f64 (sqrt.f64 (/.f64 1 x)) (hypot.f64 1 z)))
	30.2b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 y (.f64 z z) y) x) 3)))
	1.8b	(.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (/.f64 1 (.f64 y (hypot.f64 1 z))))
	7.0b	(/.f64 (/.f64 1 x) (pow.f64 (*.f64 y (fma.f64 z z 1)) 1))
	2.1b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	1.8b	(.f64 (.f64 (/.f64 1 (*.f64 y (hypot.f64 1 z))) (/.f64 1 (sqrt.f64 (hypot.f64 1 z)))) (/.f64 (/.f64 1 x) (sqrt.f64 (hypot.f64 1 z))))
	4.4b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
▶	1.7b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
	7.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))

Compiler

Compiled 9813 to 7054 computations (28.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 z)
	0.0b	(*.f64 y (hypot.f64 1 z))
	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	1.7b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`times-frac_binary64`
72×	`*-un-lft-identity_binary64`
72×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
43×	`associate-/l*_binary64`

Counts

2 → 126

Calls

2 calls:

22.0ms	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
1.0ms	(hypot.f64 1 z)

series289.0ms (3%)

Counts

2 → 48

Calls

2 calls:

280.0ms	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))
8.0ms	(hypot.f64 1 z)

simplify263.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

803×	`associate-/r*_binary64`
647×	`associate-/l*_binary64`
575×	`associate-l_binary64`
385×	`associate-*l/_binary64`
355×	`associate-/r/_binary64`

Counts

174 → 319

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	4325
1	613	3880
2	1690	3861
3	4858	3850
4	5004	3850

prune732.0ms (7.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	641	2	643
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	644	8	652

Error

Counts

652 → 8

Alt Table

Status	Error	Program
	2.5b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 1 z))) y) (/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (sqrt.f64 (hypot.f64 1 z))))
	30.2b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (fma.f64 y (.f64 z z) y) x) 3)))
	7.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	2.1b	(/.f64 (/.f64 1 (.f64 x (hypot.f64 1 z))) (.f64 y (hypot.f64 1 z)))
	2.1b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	7.0b	(/.f64 (/.f64 1 x) (pow.f64 (*.f64 y (fma.f64 z z 1)) 1))
	4.4b	(/.f64 (/.f64 (/.f64 1 (*.f64 y x)) (hypot.f64 1 z)) (hypot.f64 1 z))
✓	1.7b	(/.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) (*.f64 y (hypot.f64 1 z)))

Compiler

Compiled 8739 to 6112 computations (30.1% saved)

regimes1.8s (18.4%)

Accuracy

Total 0.9b remaining (95.5%)

Threshold costs 0.9b (95.5%)

Compiler

Compiled 18464 to 13327 computations (27.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	99
1	41	99
2	40	99

end10.0ms (0.1%)

Compiler: Compiled 210 to 147 computations (30% saved)

sample1.2s (12.3%)

Algorithm

1×

intervals

Results

442.0ms	8000×	body	128	valid
20.0ms	419×	body	128	invalid

Compiler

Compiled 236 to 169 computations (28.4% saved)

Details

analyze734.0ms (7.5%)

sample54.0ms (0.6%)

simplify32.0ms (0.3%)

prune9.0ms (0.1%)

localize13.0ms (0.1%)

rewrite30.0ms (0.3%)

series284.0ms (2.9%)

simplify273.0ms (2.8%)

prune244.0ms (2.5%)

localize22.0ms (0.2%)

rewrite49.0ms (0.5%)

series679.0ms (7%)

simplify270.0ms (2.8%)

prune537.0ms (5.5%)

localize19.0ms (0.2%)

rewrite84.0ms (0.9%)

series654.0ms (6.7%)

simplify474.0ms (4.9%)

prune932.0ms (9.6%)

localize16.0ms (0.2%)

rewrite45.0ms (0.5%)

series289.0ms (3%)

simplify263.0ms (2.7%)

prune732.0ms (7.5%)

regimes1.8s (18.4%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end10.0ms (0.1%)

sample1.2s (12.3%)

Profiling