Details

analyze98.0ms (0.9%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
25%	37.5%	37.6%	6
31.2%	31.2%	37.6%	7
37.5%	18.7%	43.8%	8
39%	15.6%	45.4%	9
42.1%	9.4%	48.5%	10
42.9%	7.8%	49.3%	11
44.5%	4.7%	50.8%	12
44.9%	3.9%	51.2%	13
45.7%	2.3%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample931.0ms (8.7%)

Results

856.0ms	8255×	body	128	valid
20.0ms	210×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
45×	`cancel-sign-sub-inv_binary64`
38×	`sub-neg_binary64`
31×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

prune3.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 35 to 22 computations (37.1% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

series8.0ms (0.1%)

Counts

1 → 15

Calls

1 calls:

8.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

709×	`distribute-rgt-in_binary64`
693×	`distribute-lft-in_binary64`
571×	`neg-mul-1_binary64`
544×	`unsub-neg_binary64`
296×	`associate-+l+_binary64`

Counts

25 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	263
1	34	241
2	94	241
3	413	241
4	2431	241
5	4317	241
6	4957	241

prune18.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.1b

Counts

26 → 4

Alt Table

Status	Error	Program
	32.1b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
▶	1.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	28.7b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 382 to 216 computations (43.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
✓	0.4b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))
✓	0.4b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))

series193.0ms (1.8%)

Counts

3 → 45

Calls

3 calls:

114.0ms

(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))

68.0ms

(cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))

11.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))

1.0ms

(cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
343×	`fma-def_binary64`
292×	`associate-r_binary64`
246×	`*-commutative_binary64`
236×	`associate-l_binary64`

Counts

138 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	5420
1	1102	4956
2	4018	4580
3	4960	4580

prune438.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	366	6	372
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	367	9	376

Error

0.0b

Counts

376 → 9

Alt Table

Status	Error	Program
	32.1b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	1.2b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))
	28.7b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
▶	1.0b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 3)
	22.8b	(.f64 (cbrt.f64 (.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	32.4b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x))) 4) (cbrt.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x)))
	1.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))

Compiler

Compiled 17372 to 10408 computations (40.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	0.4b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))
✓	0.6b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 3)

series7.1s (66.7%)

Counts

1 → 15

Calls

1 calls:

7.1s	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 3)

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`cbrt-prod_binary64`
6×	`unpow-prod-down_binary64`

Counts

1 → 32

Calls

1 calls:

2.0ms

(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) 3)

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

847×	`fma-def_binary64`
478×	`associate-l_binary64`
369×	`associate-r_binary64`
343×	`log-prod_binary64`
251×	`exp-prod_binary64`

Counts

47 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1221
1	206	953
2	570	922
3	2728	744
4	4592	744
5	4889	744

prune123.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	133	7	140

Error

0.0b

Counts

140 → 7

Alt Table

Status	Error	Program
	32.1b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	1.2b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))
	40.6b	(/.f64 (neg.f64 (sqrt.f64 x)) (/.f64 -1 y))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 3))
	28.7b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
▶	1.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 3655 to 2278 computations (37.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))
✓	0.4b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))
	0.4b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))

series173.0ms (1.6%)

Counts

2 → 30

Calls

2 calls:

105.0ms

(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))

67.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`cbrt-prod_binary64`
6×	`associate-l_binary64`
6×	`add-cube-cbrt_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 39

Calls

2 calls:

5.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))

5.0ms

(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))))

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
340×	`fma-def_binary64`
284×	`sub-neg_binary64`
257×	`associate-r_binary64`
237×	`*-commutative_binary64`

Counts

69 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	4197
1	1057	3905
2	3803	3767
3	5048	3767

prune679.0ms (6.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	461	0	461
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	461	7	468

Error

0.0b

Counts

468 → 7

Alt Table

Status	Error	Program
	32.1b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	1.2b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))
	40.6b	(/.f64 (neg.f64 (sqrt.f64 x)) (/.f64 -1 y))
	1.3b	(.f64 (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) 3))
	28.7b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
✓	1.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

Compiler

Compiled 33694 to 20267 computations (39.8% saved)

regimes307.0ms (2.9%)

Accuracy

Total 0.1b remaining (60.7%)

Threshold costs 0.1b (60.7%)

Counts

83 → 1

Compiler

Compiled 7280 to 4672 computations (35.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	14	12
2	18	12
3	20	12
4	21	12
5	20	12

end129.0ms (1.2%)

Compiler: Compiled 199 to 129 computations (35.2% saved)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Details

analyze98.0ms (0.9%)

sample931.0ms (8.7%)

simplify18.0ms (0.2%)

prune3.0ms (0%)

localize5.0ms (0%)

series8.0ms (0.1%)

rewrite1.0ms (0%)

simplify52.0ms (0.5%)

prune18.0ms (0.2%)

localize8.0ms (0.1%)

series193.0ms (1.8%)

rewrite21.0ms (0.2%)

simplify128.0ms (1.2%)

prune438.0ms (4.1%)

localize7.0ms (0.1%)

series7.1s (66.7%)

rewrite4.0ms (0%)

simplify78.0ms (0.7%)

prune123.0ms (1.2%)

localize11.0ms (0.1%)

series173.0ms (1.6%)

rewrite13.0ms (0.1%)

simplify101.0ms (1%)

prune679.0ms (6.4%)

regimes307.0ms (2.9%)

simplify2.0ms (0%)

end129.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10