Details

analyze1.2s (13%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
9.4%	89.3%	1.3%	10
13.3%	84.6%	2.1%	11
15.2%	82.3%	2.5%	12
21.1%	73.9%	5%	13
23.1%	71.1%	5.9%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample2.2s (23.5%)

Symmetry

(sort x y)

Results

1.0s	8256×	body	128	valid
900.0ms	1380×	body	8192	exit
100.0ms	823×	body	128	invalid

Compiler

Compiled 29 to 19 computations (34.5% saved)

simplify94.0ms (1%)

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%)

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

7.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.1b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	16.9b	(/.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)
✓	5.4b	(/.f64 y (fma.f64 z z z))
✓	8.7b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series193.0ms (2%)

Counts

3 → 84

Calls

3 calls:

106.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
51.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
36.0ms	(/.f64 y (fma.f64 z z z))

rewrite34.0ms (0.4%)

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:

12.0ms	(*.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))

simplify168.0ms (1.8%)

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 → 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

prune274.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	288	8	296
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	288	10	298

Error

1.6b

Counts

298 → 10

Alt Table

Status	Error	Program
	3.5b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	3.5b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
▶	3.2b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	7.3b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
	12.5b	(.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))
	37.2b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z))) (/.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
	25.5b	(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
✓	9.1b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 6301 to 1452 computations (77% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 z)
✓	4.2b	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	5.3b	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
✓	18.7b	(cbrt.f64 (fma.f64 z z z))

series2.9s (30.7%)

Counts

4 → 84

Calls

4 calls:

2.1s	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
718.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
32.0ms	(cbrt.f64 z)
8.0ms	(cbrt.f64 (fma.f64 z z z))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-exp-log_binary64`
35×	`add-cbrt-cube_binary64`
28×	`cbrt-unprod_binary64`
28×	`prod-exp_binary64`
22×	`cbrt-undiv_binary64`

Counts

4 → 98

Calls

4 calls:

15.0ms	(.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (.f64 (cbrt.f64 z) (cbrt.f64 z))))
7.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
1.0ms	(cbrt.f64 (fma.f64 z z z))
1.0ms	(cbrt.f64 z)

simplify156.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
301×	`fma-neg_binary64`
285×	`times-frac_binary64`
231×	`associate-r_binary64`
230×	`associate-l_binary64`

Counts

182 → 200

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	7046
1	925	5135
2	3568	4514
3	4932	4514
4	4963	4514

prune293.0ms (3.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	294	10	304

Error

1.6b

Counts

304 → 10

Alt Table

Status	Error	Program
▶	3.5b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	3.5b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
✓	3.2b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	7.3b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
	12.5b	(.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))
	37.2b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z))) (/.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 (fma.f64 z z z))) (sqrt.f64 z)))
	25.5b	(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
✓	9.1b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 14067 to 3745 computations (73.4% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	4.4b	(*.f64 x (/.f64 y (fma.f64 z z z)))
	5.4b	(/.f64 y (fma.f64 z z z))

series178.0ms (1.9%)

Counts

2 → 72

Calls

2 calls:

104.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
74.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite14.0ms (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:

6.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
5.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

simplify78.0ms (0.8%)

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

prune166.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	175	10	185

Error

1.4b

Counts

185 → 10

Alt Table

Status	Error	Program
✓	3.5b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
▶	3.5b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
✓	3.2b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	7.3b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
	30.6b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	25.5b	(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
✓	9.1b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	19.4b	(.f64 (sqrt.f64 (/.f64 (.f64 x (/.f64 y (fma.f64 z z z))) z)) (sqrt.f64 (/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)))

Compiler

Compiled 3274 to 925 computations (71.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.1b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
	4.4b	(*.f64 x (/.f64 y (fma.f64 z z z)))
	5.4b	(/.f64 y (fma.f64 z z z))

series110.0ms (1.2%)

Counts

1 → 36

Calls

1 calls:

109.0ms

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

rewrite13.0ms (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))

simplify69.0ms (0.7%)

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 → 82

Iterations

Useful iterations: 2 (0.0ms)

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

prune209.0ms (2.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	202	10	212

Error

1.4b

Counts

212 → 10

Alt Table

Status	Error	Program
✓	3.5b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	3.5b	(.f64 (.f64 x (/.f64 y (fma.f64 z z z))) (/.f64 1 z))
✓	3.2b	(.f64 (.f64 x (/.f64 (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) (cbrt.f64 z)))
	7.3b	(.f64 (.f64 x (/.f64 y (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 1 (fma.f64 z z z)) (cbrt.f64 z)))
	30.6b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	25.5b	(*.f64 x (-.f64 (/.f64 y (pow.f64 z 3)) (/.f64 y (pow.f64 z 4))))
	31.0b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
✓	9.1b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	19.4b	(.f64 (sqrt.f64 (/.f64 (.f64 x (/.f64 y (fma.f64 z z z))) z)) (sqrt.f64 (/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)))

Compiler

Compiled 3990 to 1361 computations (65.9% saved)

regimes856.0ms (9%)

Accuracy

Total 2.9b remaining (70%)

Threshold costs 0b (0%)

Counts

162 → 1

Compiler

Compiled 20921 to 10548 computations (49.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	58
1	19	58
2	19	58

end125.0ms (1.3%)

Compiler: Compiled 351 to 162 computations (53.8% saved)

Details

analyze1.2s (13%)

sample2.2s (23.5%)

simplify94.0ms (1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series193.0ms (2%)

rewrite34.0ms (0.4%)

simplify168.0ms (1.8%)

prune274.0ms (2.9%)

localize18.0ms (0.2%)

series2.9s (30.7%)

rewrite36.0ms (0.4%)

simplify156.0ms (1.6%)

prune293.0ms (3.1%)

localize7.0ms (0.1%)

series178.0ms (1.9%)

rewrite14.0ms (0.2%)

simplify78.0ms (0.8%)

prune166.0ms (1.7%)

localize8.0ms (0.1%)

series110.0ms (1.2%)

rewrite13.0ms (0.1%)

simplify69.0ms (0.7%)

prune209.0ms (2.2%)

regimes856.0ms (9%)

simplify3.0ms (0%)

end125.0ms (1.3%)

Profiling