Details

analyze1.2s (20.9%)

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
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)

sample1.1s (19.5%)

Results

991.0ms	8252×	body	128	valid
92.0ms	763×	body	128	invalid
1.0ms	2×	body	1024	valid
1.0ms	2×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify110.0ms (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

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	0.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series53.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
18.0ms	(/.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)

simplify83.0ms (1.4%)

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

prune113.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	129	8	137

Error

0.0b

Counts

137 → 8

Alt Table

Status	Error	Program
	18.5b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 z a)))) x)
✓	0.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	37.6b	(-.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)))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	42.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
▶	0.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
	0.5b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	31.2b	(-.f64 (fma.f64 (/.f64 (.f64 y t) a) (/.f64 z a) (fma.f64 (/.f64 y a) t x)) (/.f64 (.f64 y z) a))

Compiler

Compiled 3578 to 1195 computations (66.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z a))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
✓	0.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

series65.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

39.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
18.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
8.0ms	(/.f64 1 (-.f64 z a))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

11.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
4.0ms	(/.f64 1 (-.f64 z a))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

simplify132.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

717×	`times-frac_binary64`
517×	`cancel-sign-sub-inv_binary64`
449×	`fma-neg_binary64`
361×	`sub-neg_binary64`
182×	`+-commutative_binary64`

Counts

225 → 226

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	299	4920
1	748	4681
2	2739	4633
3	4920	4632
4	5192	4632

prune186.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	227	7	234

Error

0.0b

Counts

234 → 7

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	0.9b	(fma.f64 y (.f64 (-.f64 z t) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))) x)
✓	0.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	37.6b	(-.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)))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	42.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	31.2b	(-.f64 (fma.f64 (/.f64 (.f64 y t) a) (/.f64 z a) (fma.f64 (/.f64 y a) t x)) (/.f64 (.f64 y z) a))

Compiler

Compiled 5468 to 2036 computations (62.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	0.4b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series69.0ms (1.2%)

Counts

3 → 132

Calls

3 calls:

34.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
18.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
17.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite39.0ms (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)

simplify170.0ms (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

prune265.0ms (4.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	336	7	343

Error

0.0b

Counts

343 → 7

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
▶	0.9b	(fma.f64 y (.f64 (-.f64 z t) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))) x)
✓	0.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	37.6b	(-.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)))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	42.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	31.2b	(-.f64 (fma.f64 (/.f64 (.f64 y t) a) (/.f64 z a) (fma.f64 (/.f64 y a) t x)) (/.f64 (.f64 y z) a))

Compiler

Compiled 8774 to 2843 computations (67.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))
✓	0.4b	(fma.f64 y (.f64 (-.f64 z t) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))) x)
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
✓	0.5b	(cbrt.f64 (-.f64 z a))

series118.0ms (2%)

Counts

4 → 132

Calls

4 calls:

40.0ms	(fma.f64 y (.f64 (-.f64 z t) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))) x)
36.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
27.0ms	(cbrt.f64 (-.f64 z a))
14.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log_binary64`
85×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64`
54×	`cbrt-prod_binary64`
50×	`times-frac_binary64`

Counts

4 → 209

Calls

4 calls:

25.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))
8.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
2.0ms	(cbrt.f64 (-.f64 z a))
0.0ms	(fma.f64 y (.f64 (-.f64 z t) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))) x)

simplify206.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

384×	`fma-neg_binary64`
340×	`associate-r_binary64`
297×	`sub-neg_binary64`
269×	`associate-l_binary64`
208×	`*-commutative_binary64`

Counts

341 → 390

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	477	10100
1	1178	7669
2	4090	7217
3	4896	7217
4	4949	7217

prune425.0ms (7.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	494	0	494
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	494	7	501

Error

0.0b

Counts

501 → 7

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	0.9b	(fma.f64 y (.f64 (-.f64 z t) (.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 1 (cbrt.f64 (-.f64 z a))))) x)
✓	0.4b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	37.6b	(-.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)))))
	10.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	42.4b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	31.2b	(-.f64 (fma.f64 (/.f64 (.f64 y t) a) (/.f64 z a) (fma.f64 (/.f64 y a) t x)) (/.f64 (.f64 y z) a))

Compiler

Compiled 17557 to 7293 computations (58.5% saved)

regimes1.1s (18.6%)

Accuracy

Total 1.3b remaining (98.2%)

Threshold costs 0b (0%)

Counts

154 → 1

Compiler

Compiled 24292 to 14569 computations (40% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	17	16
2	25	16
3	29	16
4	31	16
5	31	16

end227.0ms (3.9%)

Compiler: Compiled 228 to 118 computations (48.2% saved)

Details

analyze1.2s (20.9%)

sample1.1s (19.5%)

simplify110.0ms (1.9%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series53.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify83.0ms (1.4%)

prune113.0ms (1.9%)

localize8.0ms (0.1%)

series65.0ms (1.1%)

rewrite22.0ms (0.4%)

simplify132.0ms (2.3%)

prune186.0ms (3.2%)

localize8.0ms (0.1%)

series69.0ms (1.2%)

rewrite39.0ms (0.7%)

simplify170.0ms (2.9%)

prune265.0ms (4.5%)

localize12.0ms (0.2%)

series118.0ms (2%)

rewrite58.0ms (1%)

simplify206.0ms (3.5%)

prune425.0ms (7.3%)

regimes1.1s (18.6%)

simplify3.0ms (0%)

end227.0ms (3.9%)

Profiling