Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample617.0ms (10.6%)

Infinites

0% of outputs are infinite.

Results

499.0ms	7949×	body	128	valid
24.0ms	91×	body	2048	valid
20.0ms	109×	body	1024	valid
9.0ms	64×	body	512	valid
4.0ms	43×	body	256	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify20.0ms (0.3%)

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

prune2.0ms (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 (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)

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(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)

simplify71.0ms (1.2%)

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 (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	3	22

Error

0.0b

Counts

22 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	12.4b	(*.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	(.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)))

Compiler

Compiled 345 to 162 computations (53% saved)

localize10.0ms (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))

series918.0ms (15.8%)

Counts

3 → 72

Calls

3 calls:

507.0ms

(*.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)))

404.0ms

(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 (0.3%)

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:

6.0ms

(*.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)))

4.0ms

(*.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))

simplify104.0ms (1.8%)

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

prune236.0ms (4.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	331	4	335
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	332	6	338

Error

0.0b

Counts

338 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	12.7b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	12.4b	(*.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)))
	13.2b	(.f64 (.f64 (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))))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	13.2b	(.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)))))
▶	2.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

Compiler

Compiled 11923 to 5895 computations (50.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))
✓	1.5b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)

series2.0s (34.6%)

Counts

4 → 96

Calls

4 calls:

602.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))
517.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)
444.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
441.0ms	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`

Counts

4 → 71

Calls

4 calls:

2.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
1.0ms	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))

simplify139.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary64`
614×	`times-frac_binary64`
305×	`unswap-sqr_binary64`
259×	`cancel-sign-sub-inv_binary64`
217×	`fma-neg_binary64`

Counts

167 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	4725
1	707	4573
2	2106	4228
3	4967	4228
4	4997	4228

prune145.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	159	8	167

Error

0.0b

Counts

167 → 8

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	12.7b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	12.4b	(*.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)))
	14.8b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8) (exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))))
▶	2.6b	(.f64 (.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
	13.2b	(.f64 (.f64 (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))))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	13.2b	(.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)))))
✓	2.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))

Compiler

Compiled 6270 to 3749 computations (40.2% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x)))
	1.5b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)

prune942.0ms (16.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	450	1	451
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	450	9	459

Error

0.0b

Counts

459 → 9

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)
	12.7b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))) (sqrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	12.4b	(*.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)))
	14.8b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8) (exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))))
✓	2.6b	(.f64 (.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8))) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
	13.2b	(.f64 (.f64 (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))))) (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x)))
	13.2b	(.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)))))
✓	2.5b	(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8) (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))
	14.8b	(.f64 (.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 1/2 (fabs.f64 (-.f64 y x)) x))) 8))) (exp.f64 (log.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (fabs.f64 (-.f64 y x)) 1/2 x))))))

Compiler

Compiled 29008 to 17768 computations (38.7% saved)

regimes228.0ms (3.9%)

Accuracy

Total 0.0b remaining (58.4%)

Threshold costs 0.0b (58.4%)

Counts

32 → 1

Compiler

Compiled 2549 to 1549 computations (39.2% saved)

simplify4.0ms (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

end268.0ms (4.6%)

Compiler: Compiled 303 to 185 computations (38.9% 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

analyze1.0ms (0%)

sample617.0ms (10.6%)

simplify20.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite1.0ms (0%)

simplify71.0ms (1.2%)

prune14.0ms (0.2%)

localize10.0ms (0.2%)

series918.0ms (15.8%)

rewrite19.0ms (0.3%)

simplify104.0ms (1.8%)

prune236.0ms (4.1%)

localize14.0ms (0.2%)

series2.0s (34.6%)

rewrite8.0ms (0.1%)

simplify139.0ms (2.4%)

prune145.0ms (2.5%)

localize25.0ms (0.4%)

prune942.0ms (16.2%)

regimes228.0ms (3.9%)

simplify4.0ms (0.1%)

end268.0ms (4.6%)

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