Details

analyze515.0ms (15.1%)

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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.1s (32.5%)

Results

917.0ms	8256×	body	128	valid
111.0ms	974×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify65.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
639×	`associate-/l*_binary64`
549×	`associate-/r*_binary64`
410×	`fma-neg_binary64`
343×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	17
2	55	15
3	125	15
4	273	14
5	562	11
6	1531	11
7	4085	11
8	4535	11
9	4790	11

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
▶	0.0b	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)

Compiler

Compiled 78 to 57 computations (26.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)
✓	0.0b	(/.f64 (-.f64 x z) y)

series24.0ms (0.7%)

Counts

2 → 64

Calls

2 calls:

13.0ms	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)
12.0ms	(/.f64 (-.f64 x z) y)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(/.f64 (-.f64 x z) y)
0.0ms	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)

simplify78.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1065×	`div-sub_binary64`
633×	`distribute-rgt-in_binary64`
624×	`distribute-lft-in_binary64`
539×	`times-frac_binary64`
363×	`fma-def_binary64`

Counts

114 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1334
1	232	1225
2	489	1223
3	1245	1223
4	4609	1223
5	6880	1223

prune58.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Error

Counts

81 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
	0.2b	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)
	22.1b	(fma.f64 4 (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 x z) y) (/.f64 (-.f64 x z) y)) (/.f64 (-.f64 x z) y))) 2)

Compiler

Compiled 1150 to 529 computations (54% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
✓	0.0b	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

series97.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

83.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
14.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

7.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)
5.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

simplify176.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

510×	`div-sub_binary64`
373×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`
336×	`associate-/l*_binary64`
327×	`times-frac_binary64`

Counts

114 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1603
1	306	1563
2	887	1346
3	4459	1342
4	5956	1342

prune67.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	90	3	93

Error

Counts

93 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
▶	0.2b	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)
	22.1b	(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3)))

Compiler

Compiled 1670 to 1094 computations (34.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)
✓	0.0b	(/.f64 y (-.f64 x z))
✓	0.3b	(/.f64 1 (/.f64 y (-.f64 x z)))

series76.0ms (2.2%)

Counts

3 → 96

Calls

3 calls:

46.0ms	(/.f64 y (-.f64 x z))
20.0ms	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)
10.0ms	(/.f64 1 (/.f64 y (-.f64 x z)))

rewrite40.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 159

Calls

3 calls:

7.0ms	(/.f64 1 (/.f64 y (-.f64 x z)))
4.0ms	(/.f64 y (-.f64 x z))
0.0ms	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)

simplify150.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-neg_binary64`
338×	`times-frac_binary64`
311×	`associate-/l*_binary64`
296×	`fma-def_binary64`
219×	`associate-/r*_binary64`

Counts

255 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	4096
1	417	3712
2	1184	3522
3	3945	3522
4	4959	3522
5	4983	3522

prune154.0ms (4.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	228	3	231

Error

Counts

231 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
✓	0.2b	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)
▶	22.1b	(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3)))

Compiler

Compiled 4220 to 1953 computations (53.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 (-.f64 x z) y) 1)
	0.0b	(/.f64 (-.f64 x z) y)
✓	0.2b	(pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3)
✓	20.6b	(cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3))

series87.0ms (2.6%)

Counts

3 → 108

Calls

3 calls:

54.0ms	(pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3)
16.0ms	(fma.f64 4 (/.f64 (-.f64 x z) y) 1)
16.0ms	(cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 58

Calls

3 calls:

2.0ms	(cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3))
2.0ms	(pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3)
0.0ms	(fma.f64 4 (/.f64 (-.f64 x z) y) 1)

simplify133.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
452×	`times-frac_binary64`
342×	`fma-neg_binary64`
283×	`cancel-sign-sub-inv_binary64`
246×	`sub-neg_binary64`

Counts

166 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	4283
1	458	4006
2	1693	3815
3	4433	3815
4	5055	3815

prune126.0ms (3.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	3	161

Error

Counts

161 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
✓	0.2b	(fma.f64 4 (/.f64 1 (/.f64 y (-.f64 x z))) 2)
✓	22.1b	(+.f64 1 (cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (-.f64 x z) y) 1) 3)))

Compiler

Compiled 4214 to 2572 computations (39% saved)

regimes336.0ms (9.8%)

Accuracy

Total 0.0b remaining (35.3%)

Threshold costs 0.0b (35.3%)

Counts

70 → 1

Compiler

Compiled 4726 to 3580 computations (24.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
2	19	14
3	23	14
4	26	14
5	27	14
6	27	14

end59.0ms (1.7%)

Compiler: Compiled 71 to 53 computations (25.4% saved)

Details

analyze515.0ms (15.1%)

sample1.1s (32.5%)

simplify65.0ms (1.9%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series24.0ms (0.7%)

rewrite7.0ms (0.2%)

simplify78.0ms (2.3%)

prune58.0ms (1.7%)

localize8.0ms (0.2%)

series97.0ms (2.8%)

rewrite13.0ms (0.4%)

simplify176.0ms (5.1%)

prune67.0ms (2%)

localize8.0ms (0.2%)

series76.0ms (2.2%)

rewrite40.0ms (1.2%)

simplify150.0ms (4.4%)

prune154.0ms (4.5%)

localize10.0ms (0.3%)

series87.0ms (2.6%)

rewrite8.0ms (0.2%)

simplify133.0ms (3.9%)

prune126.0ms (3.7%)

regimes336.0ms (9.8%)

simplify3.0ms (0.1%)

end59.0ms (1.7%)

Profiling