Details

analyze26.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample48.0ms (1.3%)

Algorithm

1×

intervals

Results

11.0ms	247×	body	128	valid
1.0ms	6×	body	2048	valid
0.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify20.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

97×	`fma-neg_binary64`
32×	`cancel-sign-sub-inv_binary64`
30×	`fma-def_binary64`
29×	`sub-neg_binary64`
17×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 35 to 21 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 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 (fabs.f64 (-.f64 y x)) 1/2 x)

simplify75.0ms (2%)

Algorithm

1×	egg-herbie

Rules

557×	`distribute-rgt-neg-out_binary64`
515×	`neg-mul-1_binary64`
507×	`neg-sub0_binary64`
481×	`distribute-rgt-out_binary64`
469×	`*-commutative_binary64`

Counts

34 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	374
1	26	353
2	55	353
3	125	353
4	320	353
5	990	353
6	1892	353
7	2461	353
8	3898	353
9	5066	353

prune14.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	18	4	22

Error

0.0b

Counts

22 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	19.3b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	16.4b	(expm1.f64 (log1p.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 367 to 178 computations (51.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.5b	(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

series1.0s (27.6%)

Counts

3 → 72

Calls

3 calls:

545.0ms

(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

481.0ms

(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

rewrite19.0ms (0.5%)

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 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

6.0ms

(*.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

1.0ms

(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))

simplify115.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

408×	`fma-def_binary64`
393×	`*-commutative_binary64`
356×	`cancel-sign-sub-inv_binary64`
338×	`unswap-sqr_binary64`
309×	`fma-neg_binary64`

Counts

165 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3620
1	483	3205
2	1465	3016
3	3985	2880
4	5033	2880

prune237.0ms (6.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	330	5	335
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	331	8	339

Error

0.0b

Counts

339 → 8

Alt Table

Status	Error	Program
	20.0b	(.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	19.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
	21.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (exp.f64 (log.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	19.3b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)
	16.4b	(expm1.f64 (log1p.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))

Compiler

Compiled 12045 to 5965 computations (50.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	0.5b	(cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))
✓	0.8b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

series1.1s (29.1%)

Counts

1 → 24

Calls

1 calls:

1.1s	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

rewrite3.0ms (0.1%)

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 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

simplify85.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

444×	`distribute-rgt-in_binary64`
431×	`distribute-lft-in_binary64`
409×	`associate-l_binary64`
352×	`exp-prod_binary64`
347×	`log-prod_binary64`

Counts

56 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	967
1	151	870
2	407	825
3	1831	747
4	4498	747
5	4961	747
6	4888	747

prune65.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Error

Counts

126 → 6

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 (cbrt.f64 1/8) (fma.f64 x 2 (fabs.f64 (-.f64 y x))))
	21.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (exp.f64 (log.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
	1.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	19.3b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

Compiler

Compiled 2458 to 1422 computations (42.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (fabs.f64 (-.f64 y x)))
✓	1.0b	(cbrt.f64 1/8)

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 x 2 (fabs.f64 (-.f64 y x)))
0.0ms	(cbrt.f64 1/8)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`cbrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 23

Calls

2 calls:

1.0ms	(cbrt.f64 1/8)
0.0ms	(fma.f64 x 2 (fabs.f64 (-.f64 y x)))

simplify131.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

824×	`unsub-neg_binary64`
760×	`neg-mul-1_binary64`
612×	`distribute-rgt-neg-out_binary64`
506×	`distribute-rgt-in_binary64`
503×	`distribute-lft-neg-out_binary64`

Counts

47 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	449
1	44	428
2	73	428
3	143	428
4	345	428
5	1064	428
6	2361	428
7	3024	428
8	4363	428
9	4979	428
10	5000	428
11	4999	428
12	4871	428

prune17.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	31	6	37

Error

Counts

37 → 6

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 (cbrt.f64 1/8) (fma.f64 x 2 (fabs.f64 (-.f64 y x))))
	21.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (exp.f64 (log.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))))
	1.4b	(.f64 (cbrt.f64 1/8) (.f64 (*.f64 (cbrt.f64 (fma.f64 x 2 (fabs.f64 (-.f64 y x)))) (cbrt.f64 (fma.f64 x 2 (fabs.f64 (-.f64 y x))))) (cbrt.f64 (fma.f64 x 2 (fabs.f64 (-.f64 y x))))))
✓	0.0b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	19.3b	(*.f64 (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) (sqrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)) 3)

Compiler

Compiled 528 to 313 computations (40.7% saved)

regimes102.0ms (2.7%)

Accuracy

Total 0.0b remaining (74.1%)

Threshold costs 0.0b (74.1%)

Counts

29 → 1

Compiler

Compiled 2336 to 1363 computations (41.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`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	7	10
1	11	10
2	18	10
3	23	10
4	26	10
5	27	10
6	27	10

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample617.0ms (16.5%)

Algorithm

1×

intervals

Results

265.0ms	7721×	body	128	valid
12.0ms	90×	body	2048	valid
11.0ms	103×	body	1024	valid
5.0ms	63×	body	512	valid
1.0ms	23×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 135 to 86 computations (36.3% saved)

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10

Details

analyze26.0ms (0.7%)

sample48.0ms (1.3%)

simplify20.0ms (0.5%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify75.0ms (2%)

prune14.0ms (0.4%)

localize8.0ms (0.2%)

series1.0s (27.6%)

rewrite19.0ms (0.5%)

simplify115.0ms (3.1%)

prune237.0ms (6.3%)

localize7.0ms (0.2%)

series1.1s (29.1%)

rewrite3.0ms (0.1%)

simplify85.0ms (2.3%)

prune65.0ms (1.7%)

localize8.0ms (0.2%)

series4.0ms (0.1%)

rewrite2.0ms (0%)

simplify131.0ms (3.5%)

prune17.0ms (0.4%)

regimes102.0ms (2.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample617.0ms (16.5%)

Profiling

Iter	Nodes	Cost
0	8	12
1	13	12
2	20	12
3	29	12
4	45	12
5	79	12
6	97	12
7	123	12
8	174	10
9	188	10
10	229	10
11	263	10
12	283	10
13	291	10
14	296	10
15	256	10