Details

analyze943.0ms (7.9%)

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
19.5%	76.8%	3.7%	12
25.7%	64.7%	9.6%	13
31.6%	54.7%	13.7%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.6s (13.3%)

Results

1.1s	8256×	body	128	valid
399.0ms	2689×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify179.0ms (1.5%)

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

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

0.0b

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)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.1%)

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)

simplify72.0ms (0.6%)

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

prune24.0ms (0.2%)

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

0.0b

Counts

38 → 4

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)))
	32.0b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (-.f64 t x) x)))

Compiler

Compiled 573 to 160 computations (72.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series83.0ms (0.7%)

Counts

4 → 87

Calls

4 calls:

53.0ms	(+.f64 (.f64 y x) (.f64 t z))
17.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
9.0ms	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
4.0ms	(+.f64 (*.f64 z x) x)

rewrite56.0ms (0.5%)

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:

33.0ms	(+.f64 (.f64 y x) (.f64 t z))
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))
3.0ms	(+.f64 (*.f64 z x) x)

simplify107.0ms (0.9%)

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

prune127.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	172	3	175

Error

0.0b

Counts

175 → 3

Alt Table

Status	Error	Program
	48.4b	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 t z) 3)))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (*.f64 t z))))))
▶	31.9b	(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	(fma.f64 (-.f64 y z) (-.f64 t x) x)

Compiler

Compiled 5008 to 721 computations (85.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 z x) x)
	0.0b	(+.f64 (.f64 y t) (+.f64 (.f64 z x) x))
✓	0.0b	(sqrt.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)))
✓	0.2b	(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 (10.7%)

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))))

126.0ms

(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:

4.0ms

(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))))

simplify95.0ms (0.8%)

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

prune141.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	257	3	260

Error

0.0b

Counts

260 → 3

Alt Table

Status	Error	Program
▶	48.4b	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 t z) 3)))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (*.f64 t z))))))
✓	31.9b	(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	(fma.f64 (-.f64 y z) (-.f64 t x) x)

Compiler

Compiled 9784 to 1832 computations (81.3% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z)))))
✓	6.5b	(.f64 (.f64 y x) (*.f64 t z))
✓	15.6b	(-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (*.f64 t z) 3))))
✓	44.6b	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 t z) 3)))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (*.f64 t z))))))

series3.9s (32.6%)

Counts

4 → 192

Calls

4 calls:

3.5s	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 t z) 3)))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (*.f64 t z))))))
311.0ms	(-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (*.f64 t z) 3))))
119.0ms	(.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z)))))
19.0ms	(.f64 (.f64 y x) (*.f64 t z))

rewrite256.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`frac-times_binary64`
128×	`frac-sub_binary64`
104×	`flip--_binary64`
104×	`flip3--_binary64`
102×	`flip-+_binary64`

Counts

4 → 237

Calls

4 calls:

49.0ms	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 t z) 3)))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (*.f64 t z))))))
19.0ms	(-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (*.f64 t z) 3))))
15.0ms	(.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z)))))
6.0ms	(.f64 (.f64 y x) (*.f64 t z))

simplify770.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
366×	`times-frac_binary64`
148×	`sub-neg_binary64`
88×	`fma-neg_binary64`
18×	`cube-mult_binary64`

Counts

429 → 587

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3173	86844
1	5054	86844

prune1.3s (10.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	609	0	609
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	609	3	612

Error

0.0b

Counts

612 → 3

Alt Table

Status	Error	Program
✓	48.4b	(/.f64 (-.f64 (.f64 (-.f64 (.f64 (.f64 y t) (.f64 y t)) (.f64 (+.f64 (.f64 z x) x) (+.f64 (.f64 z x) x))) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (.f64 t z))))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (.f64 t z) 3)))) (.f64 (-.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (.f64 t z) (.f64 t z)) (.f64 (.f64 y x) (*.f64 t z))))))
✓	31.9b	(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	(fma.f64 (-.f64 y z) (-.f64 t x) x)

Compiler

Compiled 161396 to 42458 computations (73.7% saved)

regimes904.0ms (7.5%)

Accuracy

Total 0.0b remaining (34.1%)

Threshold costs 0.0b (34.1%)

Counts

140 → 1

Compiler

Compiled 25976 to 12160 computations (53.2% 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

end63.0ms (0.5%)

Compiler: Compiled 171 to 62 computations (63.7% saved)

Details

analyze943.0ms (7.9%)

sample1.6s (13.3%)

simplify179.0ms (1.5%)

prune2.0ms (0%)

localize5.0ms (0%)

series13.0ms (0.1%)

rewrite1.0ms (0%)

simplify72.0ms (0.6%)

prune24.0ms (0.2%)

localize11.0ms (0.1%)

series83.0ms (0.7%)

rewrite56.0ms (0.5%)

simplify107.0ms (0.9%)

prune127.0ms (1.1%)

localize13.0ms (0.1%)

series1.3s (10.7%)

rewrite6.0ms (0.1%)

simplify95.0ms (0.8%)

prune141.0ms (1.2%)

localize29.0ms (0.2%)

series3.9s (32.6%)

rewrite256.0ms (2.1%)

simplify770.0ms (6.4%)

prune1.3s (10.9%)

regimes904.0ms (7.5%)

simplify3.0ms (0%)

end63.0ms (0.5%)

Profiling