Details

analyze914.0ms (19.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
12.5%	85.6%	1.9%	11
19.8%	76.5%	3.7%	12
26.1%	64.4%	9.6%	13
31.7%	54.5%	13.7%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample101.0ms (2.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	77×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify190.0ms (4%)

Algorithm

1×	egg-herbie

Rules

2262×	`fma-neg_binary64`
697×	`fma-def_binary64`
683×	`unsub-neg_binary64`
313×	`distribute-rgt-in_binary64`
306×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	37	11
3	105	11
4	335	11
5	850	11
6	1678	11
7	1991	11
8	2282	11
9	2193	11
10	2201	11
11	2201	11
12	2202	11
13	2172	11
14	2172	11
15	4437	11
16	4437	11
17	4437	11
18	4378	11

prune4.0ms (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 (-.f64 y z) (-.f64 t x) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)

series12.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

12.0ms

(fma.f64 (-.f64 y z) (-.f64 t x) 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 (-.f64 y z) (-.f64 t x) x)

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
395×	`exp-diff_binary64`
356×	`unsub-neg_binary64`
333×	`exp-prod_binary64`
328×	`distribute-neg-out_binary64`

Counts

58 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	954
1	144	926
2	355	926
3	837	628
4	2944	628
5	4449	628
6	4978	628

prune25.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
	32.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))
▶	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
	43.8b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 537 to 160 computations (70.2% saved)

localize105.0ms (2.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
✓	0.0b	(+.f64 (.f64 y x) (.f64 t z))
✓	0.0b	(+.f64 (*.f64 z x) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))

series187.0ms (4%)

Counts

4 → 87

Calls

4 calls:

153.0ms	(+.f64 (*.f64 z x) x)
15.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
10.0ms	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
8.0ms	(+.f64 (.f64 y x) (.f64 t z))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-log-exp_binary64`
15×	`*-un-lft-identity_binary64`
14×	`sum-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

10.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
5.0ms	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
4.0ms	(+.f64 (.f64 y x) (.f64 t z))
3.0ms	(+.f64 (*.f64 z x) x)

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-neg_binary64`
411×	`cancel-sign-sub-inv_binary64`
239×	`distribute-rgt-neg-in_binary64`
204×	`associate-l_binary64`
202×	`distribute-lft-neg-in_binary64`

Counts

174 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2841
1	581	2709
2	2510	2561
3	4444	2561
4	4931	2561

prune98.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Error

Counts

175 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
▶	32.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
	43.8b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 4847 to 691 computations (85.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
✓	0.1b	(sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x))
✓	0.2b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))

series680.0ms (14.5%)

Counts

2 → 64

Calls

2 calls:

667.0ms	(sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x))
13.0ms	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

6.0ms	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))
1.0ms	(sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x))

simplify106.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-r_binary64`
480×	`associate-l_binary64`
404×	`fma-def_binary64`
323×	`*-commutative_binary64`
261×	`fma-neg_binary64`

Counts

132 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	4680
1	1106	4168
2	4190	4108
3	5203	4108

prune159.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	253	4	257

Error

Counts

257 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
✓	32.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
▶	43.8b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 11682 to 3711 computations (68.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (-.f64 t x) (-.f64 y z) x)
✓	0.2b	(pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3)
✓	41.2b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

series310.0ms (6.6%)

Counts

3 → 144

Calls

3 calls:

283.0ms	(pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3)
14.0ms	(fma.f64 (-.f64 t x) (-.f64 y z) x)
12.0ms	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

rewrite6.0ms (0.1%)

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:

1.0ms	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))
1.0ms	(pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3)
0.0ms	(fma.f64 (-.f64 t x) (-.f64 y z) x)

simplify197.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1006×	`fma-def_binary64`
652×	`associate-+l+_binary64`
415×	`associate-r_binary64`
297×	`associate-l_binary64`
271×	`+-commutative_binary64`

Counts

202 → 157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	480	14656
1	1656	14368
2	5379	14368

prune163.0ms (3.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	157	4	161

Error

Counts

161 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
✓	32.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
✓	43.8b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 9623 to 5417 computations (43.7% saved)

regimes397.0ms (8.5%)

Accuracy

Total 0.0b remaining (78.8%)

Threshold costs 0.0b (78.8%)

Counts

67 → 1

Compiler

Compiled 6927 to 4098 computations (40.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	19	23
2	28	23
3	48	23
4	61	23
5	71	23
6	75	23
7	75	23

end0.0ms (0%)

Compiler: Compiled 20 to 11 computations (45% saved)

sample797.0ms (17%)

Algorithm

1×

intervals

Results

289.0ms	8000×	body	128	valid
93.0ms	2539×	body	128	invalid

Compiler

Compiled 109 to 62 computations (43.1% saved)

Details

analyze914.0ms (19.5%)

sample101.0ms (2.2%)

simplify190.0ms (4%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify75.0ms (1.6%)

prune25.0ms (0.5%)

localize105.0ms (2.2%)

series187.0ms (4%)

rewrite27.0ms (0.6%)

simplify100.0ms (2.1%)

prune98.0ms (2.1%)

localize9.0ms (0.2%)

series680.0ms (14.5%)

rewrite14.0ms (0.3%)

simplify106.0ms (2.3%)

prune159.0ms (3.4%)

localize9.0ms (0.2%)

series310.0ms (6.6%)

rewrite6.0ms (0.1%)

simplify197.0ms (4.2%)

prune163.0ms (3.5%)

regimes397.0ms (8.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample797.0ms (17%)

Profiling