Details

analyze1.6s (22.2%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.5s (20.5%)

Results

1.1s	8252×	body	128	valid
235.0ms	361×	body	8192	exit
53.0ms	397×	body	128	invalid
2.0ms	1×	body	2048	valid
1.0ms	2×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify115.0ms (1.6%)

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
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	9.7b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

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))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series59.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

39.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
20.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite15.0ms (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)

simplify94.0ms (1.3%)

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

prune112.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	133	4	137

Error

0.0b

Counts

137 → 4

Alt Table

Status	Error	Program
	37.3b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
▶	9.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))

Compiler

Compiled 3388 to 1099 computations (67.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
✓	3.9b	(/.f64 (*.f64 y t) (-.f64 z a))
✓	10.3b	(/.f64 (*.f64 y z) (-.f64 z a))

series96.0ms (1.3%)

Counts

3 → 81

Calls

3 calls:

47.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
28.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
20.0ms	(/.f64 (*.f64 y z) (-.f64 z a))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
44×	`prod-diff_binary64`
35×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`

Counts

3 → 137

Calls

3 calls:

15.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
7.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
5.0ms	(/.f64 (*.f64 y z) (-.f64 z a))

simplify148.0ms (2%)

Algorithm

1×	egg-herbie

Rules

570×	`cancel-sign-sub-inv_binary64`
266×	`sub-neg_binary64`
221×	`associate-/l*_binary64`
212×	`fma-neg_binary64`
193×	`times-frac_binary64`

Counts

218 → 239

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	380	8392
1	1001	6278
2	3795	5703
3	5105	5703

prune298.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	238	5	243

Error

Counts

243 → 5

Alt Table

Status	Error	Program
▶	5.7b	(-.f64 (+.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a)))) x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	37.3b	(-.f64 (+.f64 (fma.f64 (/.f64 a (/.f64 z a)) (/.f64 y z) (fma.f64 (/.f64 a z) y y)) x) (fma.f64 (/.f64 (.f64 y a) z) (/.f64 t z) (fma.f64 (/.f64 y z) t (/.f64 (.f64 y (.f64 a (.f64 a t))) (pow.f64 z 3)))))
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	9.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (.f64 (*.f64 y t) (/.f64 1 (-.f64 z a))))

Compiler

Compiled 8367 to 1660 computations (80.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
✓	0.6b	(cbrt.f64 (-.f64 z a))
	3.9b	(/.f64 (*.f64 y t) (-.f64 z a))
✓	7.4b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a))))

series133.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

70.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
35.0ms	(cbrt.f64 (-.f64 z a))
27.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a))))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
50×	`cbrt-prod_binary64`
38×	`associate-r_binary64`
34×	`times-frac_binary64`

Counts

3 → 152

Calls

3 calls:

22.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a))))
9.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
4.0ms	(cbrt.f64 (-.f64 z a))

simplify171.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
328×	`associate-r_binary64`
285×	`associate-l_binary64`
239×	`*-commutative_binary64`
201×	`associate-*r/_binary64`

Counts

236 → 266

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	6426
1	1080	5591
2	4105	5499
3	4986	5499
4	4969	5499

prune363.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	425	1	426
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	426	5	431

Error

Counts

431 → 5

Alt Table

Status	Error	Program
✓	5.7b	(-.f64 (+.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a)))) x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	3.5b	(-.f64 (+.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a)))) x) (/.f64 y (/.f64 (-.f64 z a) t)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	9.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (.f64 (*.f64 y t) (/.f64 1 (-.f64 z a))))

Compiler

Compiled 17494 to 5082 computations (71% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
	0.6b	(cbrt.f64 (-.f64 z a))
✓	5.4b	(/.f64 y (/.f64 (-.f64 z a) t))
	7.4b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a))))

series29.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

29.0ms

(/.f64 y (/.f64 (-.f64 z a) t))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`times-frac_binary64`
81×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
57×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

1 → 96

Calls

1 calls:

6.0ms

(/.f64 y (/.f64 (-.f64 z a) t))

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
541×	`associate-/r/_binary64`
514×	`associate-/r*_binary64`
511×	`associate-*l/_binary64`
279×	`fma-def_binary64`

Counts

144 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	3209
1	578	3125
2	1831	2966
3	4806	2965
4	5000	2965
5	4975	2965

prune439.0ms (6.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	516	0	516
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	516	5	521

Error

Counts

521 → 5

Alt Table

Status	Error	Program
✓	5.7b	(-.f64 (+.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a)))) x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	3.5b	(-.f64 (+.f64 (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 z (cbrt.f64 (-.f64 z a)))) x) (/.f64 y (/.f64 (-.f64 z a) t)))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	9.7b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (.f64 (*.f64 y t) (/.f64 1 (-.f64 z a))))

Compiler

Compiled 20992 to 5454 computations (74% saved)

regimes1.7s (23.3%)

Accuracy

Total 0.3b remaining (94.2%)

Threshold costs 0.3b (94.2%)

Counts

161 → 3

Compiler

Compiled 27876 to 15759 computations (43.5% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
9×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	103
1	47	103
2	64	103
3	80	103
4	88	103
5	90	103
6	89	103

end88.0ms (1.2%)

Compiler: Compiled 283 to 124 computations (56.2% saved)

Details

analyze1.6s (22.2%)

sample1.5s (20.5%)

simplify115.0ms (1.6%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series59.0ms (0.8%)

rewrite15.0ms (0.2%)

simplify94.0ms (1.3%)

prune112.0ms (1.5%)

localize10.0ms (0.1%)

series96.0ms (1.3%)

rewrite41.0ms (0.6%)

simplify148.0ms (2%)

prune298.0ms (4.1%)

localize16.0ms (0.2%)

series133.0ms (1.8%)

rewrite53.0ms (0.7%)

simplify171.0ms (2.4%)

prune363.0ms (5%)

localize16.0ms (0.2%)

series29.0ms (0.4%)

rewrite18.0ms (0.2%)

simplify129.0ms (1.8%)

prune439.0ms (6.1%)

regimes1.7s (23.3%)

bsearch7.0ms (0.1%)

simplify6.0ms (0.1%)

end88.0ms (1.2%)

Profiling