Details

analyze1.2s (20.4%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (20%)

Results

1.0s	8254×	body	128	valid
100.0ms	756×	body	128	invalid
1.0ms	2×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
▶	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series73.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

43.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
30.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune109.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	5	137

Error

Counts

137 → 5

Alt Table

Status	Error	Program
	19.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
	36.5b	(*.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))))
	10.3b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
	4.8b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

Compiler

Compiled 3375 to 1106 computations (67.2% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series83.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
21.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
21.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify171.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune253.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	336	5	341

Error

Counts

341 → 5

Alt Table

Status	Error	Program
	10.3b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
	4.8b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	19.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
✓	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
▶	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

Compiler

Compiled 8597 to 2766 computations (67.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
✓	0.0b	(/.f64 t (-.f64 z a))
✓	0.0b	(/.f64 z (-.f64 z a))
✓	1.0b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

series109.0ms (1.8%)

Counts

4 → 135

Calls

4 calls:

53.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)
27.0ms	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
20.0ms	(/.f64 t (-.f64 z a))
9.0ms	(/.f64 z (-.f64 z a))

rewrite162.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

728×	`*-un-lft-identity_binary64`
718×	`add-sqr-sqrt_binary64`
708×	`times-frac_binary64`
441×	`prod-diff_binary64`
422×	`add-cube-cbrt_binary64`

Counts

4 → 601

Calls

4 calls:

32.0ms	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
4.0ms	(/.f64 z (-.f64 z a))
4.0ms	(/.f64 t (-.f64 z a))
0.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

simplify616.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

307×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
261×	`fma-neg_binary64`
256×	`associate-+r-_binary64`
194×	`associate-/l*_binary64`

Counts

736 → 666

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	727	47251
1	1706	27729
2	4438	26919
3	5006	26919

prune477.0ms (8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	666	0	666
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	666	5	671

Error

Counts

671 → 5

Alt Table

Status	Error	Program
	10.3b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
▶	4.8b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	19.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
✓	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

Compiler

Compiled 31844 to 5840 computations (81.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	0.0b	(/.f64 y (-.f64 z a))
✓	1.7b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	4.3b	(/.f64 (*.f64 y t) (-.f64 z a))

series126.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

52.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
30.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
24.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)
19.0ms	(/.f64 y (-.f64 z a))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
33×	`prod-diff_binary64`

Counts

4 → 141

Calls

4 calls:

11.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
5.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
4.0ms	(/.f64 y (-.f64 z a))
0.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)

simplify217.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

540×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
252×	`sub-neg_binary64`
206×	`associate-/l*_binary64`
189×	`times-frac_binary64`

Counts

297 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7851
1	956	7082
2	3439	6648
3	4776	6648
4	4997	6648
5	4858	6648

prune174.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	265	5	270

Error

Counts

270 → 5

Alt Table

Status	Error	Program
	10.3b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
✓	4.8b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	19.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
✓	1.1b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

Compiler

Compiled 8488 to 1726 computations (79.7% saved)

regimes569.0ms (9.5%)

Accuracy

Total 1.3b remaining (98%)

Threshold costs 0b (0%)

Counts

86 → 1

Compiler

Compiled 10670 to 6554 computations (38.6% 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	12	14
1	18	14
2	25	14
3	29	14
4	31	14
5	30	14

end79.0ms (1.3%)

Compiler: Compiled 130 to 73 computations (43.8% saved)

Details

analyze1.2s (20.4%)

sample1.2s (20%)

simplify114.0ms (1.9%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series73.0ms (1.2%)

rewrite11.0ms (0.2%)

simplify90.0ms (1.5%)

prune109.0ms (1.8%)

localize13.0ms (0.2%)

series83.0ms (1.4%)

rewrite40.0ms (0.7%)

simplify171.0ms (2.9%)

prune253.0ms (4.2%)

localize8.0ms (0.1%)

series109.0ms (1.8%)

rewrite162.0ms (2.7%)

simplify616.0ms (10.3%)

prune477.0ms (8%)

localize14.0ms (0.2%)

series126.0ms (2.1%)

rewrite31.0ms (0.5%)

simplify217.0ms (3.6%)

prune174.0ms (2.9%)

regimes569.0ms (9.5%)

simplify3.0ms (0%)

end79.0ms (1.3%)

Profiling