Details

analyze1.9s (7.1%)

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)

sample48.0ms (0.2%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
5.0ms	81×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify194.0ms (0.7%)

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

prune5.0ms (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

0.0b

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)

localize11.0ms (0%)

Local error

Found 1 expressions with local error:

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

series29.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

29.0ms

(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:

1.0ms

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

simplify107.0ms (0.4%)

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

prune44.0ms (0.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	2	38

Error

0.0b

Counts

38 → 2

Alt Table

Status	Error	Program
✓	0.0b	(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)))

Compiler

Compiled 461 to 122 computations (73.5% saved)

localize25.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))

series38.0ms (0.1%)

Counts

2 → 45

Calls

2 calls:

31.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
7.0ms	(+.f64 (*.f64 z x) x)

rewrite40.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-log-exp_binary64`
13×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`sum-log_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 57

Calls

2 calls:

24.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
6.0ms	(+.f64 (*.f64 z x) x)

simplify153.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

704×	`times-frac_binary64`
391×	`cancel-sign-sub-inv_binary64`
244×	`fma-neg_binary64`
223×	`distribute-rgt-neg-in_binary64`
193×	`associate-l_binary64`

Counts

102 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2172
1	567	2040
2	2340	1892
3	4528	1892
4	5944	1892

prune147.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	108	5	113

Error

0.0b

Counts

113 → 5

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
	35.7b	(+.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 y x) (.f64 t z)))) (sqrt.f64 (+.f64 (.f64 y x) (*.f64 t z)))))
	33.0b	(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))))
▶	0.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))) (cbrt.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)))

Compiler

Compiled 3643 to 583 computations (84% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 z x) x)
✓	0.2b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))) (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (neg.f64 (fma.f64 z t (.f64 x y))))
✓	0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (*.f64 z x) x))))
✓	0.5b	(cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))

series20.1s (73.9%)

Counts

3 → 144

Calls

3 calls:

19.2s

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

696.0ms

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

279.0ms

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

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`cbrt-div_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 75

Calls

3 calls:

13.0ms

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

6.0ms

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

0.0ms

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

simplify270.0ms (1%)

Algorithm

1×	egg-herbie

Rules

371×	`fma-def_binary64`
306×	`associate-+r+_binary64`
302×	`associate-r_binary64`
227×	`associate-/l*_binary64`
226×	`associate-*r/_binary64`

Counts

219 → 370

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1690	23988
1	5414	23988

prune927.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	676	0	676
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	676	5	681

Error

0.0b

Counts

681 → 5

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
	35.7b	(+.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 y x) (.f64 t z)))) (sqrt.f64 (+.f64 (.f64 y x) (*.f64 t z)))))
▶	33.0b	(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))))
✓	0.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))) (cbrt.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)))

Compiler

Compiled 63803 to 27664 computations (56.6% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	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))))

series1.3s (4.9%)

Counts

2 → 40

Calls

2 calls:

1.2s

(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))))

131.0ms

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

rewrite7.0ms (0%)

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))))

simplify101.0ms (0.4%)

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

prune117.0ms (0.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	191	5	196

Error

0.0b

Counts

196 → 5

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
	35.7b	(+.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 y x) (.f64 t z)))) (sqrt.f64 (+.f64 (.f64 y x) (*.f64 t z)))))
✓	33.0b	(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))))
✓	0.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x))) (cbrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))) (cbrt.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)))

Compiler

Compiled 7518 to 1658 computations (77.9% saved)

regimes689.0ms (2.5%)

Accuracy

Total 0.0b remaining (63%)

Threshold costs 0.0b (63%)

Counts

100 → 1

Compiler

Compiled 17204 to 7600 computations (55.8% saved)

simplify3.0ms (0%)

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	8	11
1	12	11
2	20	11
3	24	11
4	26	11
5	26	11

end0.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample810.0ms (3%)

Algorithm

1×

intervals

Results

280.0ms	8000×	body	128	valid
94.0ms	2454×	body	128	invalid

Compiler

Compiled 170 to 81 computations (52.4% saved)

Details

analyze1.9s (7.1%)

sample48.0ms (0.2%)

simplify194.0ms (0.7%)

prune5.0ms (0%)

localize11.0ms (0%)

series29.0ms (0.1%)

rewrite1.0ms (0%)

simplify107.0ms (0.4%)

prune44.0ms (0.2%)

localize25.0ms (0.1%)

series38.0ms (0.1%)

rewrite40.0ms (0.1%)

simplify153.0ms (0.6%)

prune147.0ms (0.5%)

localize28.0ms (0.1%)

series20.1s (73.9%)

rewrite26.0ms (0.1%)

simplify270.0ms (1%)

prune927.0ms (3.4%)

localize12.0ms (0%)

series1.3s (4.9%)

rewrite7.0ms (0%)

simplify101.0ms (0.4%)

prune117.0ms (0.4%)

regimes689.0ms (2.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample810.0ms (3%)

Profiling