Details

analyze824.0ms (16.5%)

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)

sample112.0ms (2.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	74×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify164.0ms (3.3%)

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

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 (-.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)

series14.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

14.0ms

(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)

simplify70.0ms (1.4%)

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

prune24.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Error

0.0b

Counts

38 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 491 to 142 computations (71.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series42.0ms (0.8%)

Counts

4 → 87

Calls

4 calls:

18.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
12.0ms	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
8.0ms	(+.f64 (.f64 y x) (.f64 t z))
4.0ms	(+.f64 (*.f64 z x) x)

rewrite30.0ms (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:

12.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
7.0ms	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
3.0ms	(+.f64 (.f64 y x) (.f64 t z))
3.0ms	(+.f64 (*.f64 z x) x)

simplify98.0ms (2%)

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

prune106.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
▶	32.0b	(fma.f64 (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (neg.f64 (fma.f64 z t (*.f64 x y))))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 4865 to 699 computations (85.6% saved)

localize13.0ms (0.3%)

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 z x) x)
✓	0.0b	(sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))
✓	0.1b	(fma.f64 (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (neg.f64 (fma.f64 z t (*.f64 x y))))

series1.2s (24.5%)

Counts

2 → 40

Calls

2 calls:

1.1s

(fma.f64 (sqrt.f64 (+.f64 (*.f64 y t) (+.f64 (*.f64 z x) x))) (sqrt.f64 (+.f64 (*.f64 y t) (+.f64 (*.f64 z x) x))) (neg.f64 (fma.f64 z t (*.f64 x y))))

125.0ms

(sqrt.f64 (+.f64 (*.f64 y t) (+.f64 (*.f64 z x) x)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64`
3×	`sqrt-prod_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 27

Calls

2 calls:

5.0ms

(sqrt.f64 (+.f64 (*.f64 y t) (+.f64 (*.f64 z x) x)))

0.0ms

(fma.f64 (sqrt.f64 (+.f64 (*.f64 y t) (+.f64 (*.f64 z x) x))) (sqrt.f64 (+.f64 (*.f64 y t) (+.f64 (*.f64 z x) x))) (neg.f64 (fma.f64 z t (*.f64 x y))))

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

432×	`cancel-sign-sub-inv_binary64`
339×	`associate-+l+_binary64`
259×	`associate--l+_binary64`
242×	`distribute-rgt-in_binary64`
220×	`distribute-lft-in_binary64`

Counts

67 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1773
1	501	1698
2	1746	1628
3	4940	1628
4	4999	1628
5	4973	1628

prune139.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	257	4	261

Error

Counts

261 → 4

Alt Table

Status	Error	Program
✓	32.0b	(fma.f64 (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (neg.f64 (fma.f64 z t (*.f64 x y))))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
▶	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 9653 to 1814 computations (81.2% saved)

localize8.0ms (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)
✓	38.7b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

series280.0ms (5.6%)

Counts

3 → 144

Calls

3 calls:

255.0ms	(pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3)
12.0ms	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))
12.0ms	(fma.f64 (-.f64 t x) (-.f64 y z) x)

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:

2.0ms	(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)

simplify204.0ms (4.1%)

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

prune162.0ms (3.2%)

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
✓	32.0b	(fma.f64 (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (neg.f64 (fma.f64 z t (*.f64 x y))))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
✓	41.0b	(cbrt.f64 (pow.f64 (fma.f64 (-.f64 t x) (-.f64 y z) x) 3))

Compiler

Compiled 9632 to 5421 computations (43.7% saved)

regimes493.0ms (9.8%)

Accuracy

Total 0.0b remaining (80.3%)

Threshold costs 0.0b (80.3%)

Counts

80 → 1

Compiler

Compiled 9769 to 5147 computations (47.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	21	20
2	34	20
3	42	20
4	47	20
5	48	20
6	48	20

end0.0ms (0%)

Compiler: Compiled 18 to 10 computations (44.4% saved)

sample869.0ms (17.3%)

Algorithm

1×

intervals

Results

300.0ms	8000×	body	128	valid
96.0ms	2539×	body	128	invalid

Compiler

Compiled 116 to 65 computations (44% saved)

Details

analyze824.0ms (16.5%)

sample112.0ms (2.2%)

simplify164.0ms (3.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series14.0ms (0.3%)

rewrite1.0ms (0%)

simplify70.0ms (1.4%)

prune24.0ms (0.5%)

localize13.0ms (0.3%)

series42.0ms (0.8%)

rewrite30.0ms (0.6%)

simplify98.0ms (2%)

prune106.0ms (2.1%)

localize13.0ms (0.3%)

series1.2s (24.5%)

rewrite6.0ms (0.1%)

simplify92.0ms (1.8%)

prune139.0ms (2.8%)

localize8.0ms (0.2%)

series280.0ms (5.6%)

rewrite6.0ms (0.1%)

simplify204.0ms (4.1%)

prune162.0ms (3.2%)

regimes493.0ms (9.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample869.0ms (17.3%)

Profiling