Details

analyze1.2s (24.8%)

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 (23.9%)

Results

1.0s	8256×	body	128	valid
87.0ms	718×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify123.0ms (2.5%)

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)
	10.3b	(+.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))
✓	1.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series49.0ms (1%)

Counts

2 → 96

Calls

2 calls:

34.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
15.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite13.0ms (0.3%)

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:

8.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify86.0ms (1.7%)

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 (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	129	6	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	130	7	137

Error

0.0b

Counts

137 → 7

Alt Table

Status	Error	Program
	5.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	10.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
	21.6b	(fma.f64 (/.f64 y a) t x)
	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
▶	1.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	29.5b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (sqrt.f64 (-.f64 z a))) (/.f64 (cbrt.f64 (-.f64 z t)) (sqrt.f64 (-.f64 z a)))) x)

Compiler

Compiled 3424 to 1137 computations (66.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.2b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series70.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

34.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
19.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
16.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite43.0ms (0.9%)

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)

simplify188.0ms (3.8%)

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

prune273.0ms (5.5%)

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
	5.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	10.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
	21.6b	(fma.f64 (/.f64 y a) t x)
▶	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
✓	1.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	29.5b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (sqrt.f64 (-.f64 z a))) (/.f64 (cbrt.f64 (-.f64 z t)) (sqrt.f64 (-.f64 z a)))) x)

Compiler

Compiled 8644 to 2797 computations (67.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z a))
✓	0.3b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
✓	1.2b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

series57.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

34.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
16.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
7.0ms	(/.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:

10.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a)))
6.0ms	(/.f64 1 (-.f64 z a))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)

simplify138.0ms (2.8%)

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

prune181.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	226	0	226
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	226	7	233

Error

0.0b

Counts

233 → 7

Alt Table

Status	Error	Program
▶	5.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	10.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
	21.6b	(fma.f64 (/.f64 y a) t x)
✓	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
✓	1.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	29.5b	(fma.f64 y (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (sqrt.f64 (-.f64 z a))) (/.f64 (cbrt.f64 (-.f64 z t)) (sqrt.f64 (-.f64 z a)))) x)

Compiler

Compiled 5304 to 1968 computations (62.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z a))
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	2.5b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	4.4b	(/.f64 (*.f64 y t) (-.f64 z a))

series105.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
24.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
21.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)
15.0ms	(/.f64 y (-.f64 z a))

rewrite26.0ms (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:

7.0ms	(-.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 (4.3%)

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

prune206.0ms (4.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	2	1	3
Picked	0	1	1
Done	1	2	3
Total	266	6	272

Error

Counts

272 → 6

Alt Table

Status	Error	Program
✓	5.6b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	3.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
	10.9b	(fma.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 z a)) 3)) x)
	26.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (.f64 (sqrt.f64 (/.f64 (.f64 y t) (-.f64 z a))) (sqrt.f64 (/.f64 (*.f64 y t) (-.f64 z a)))))
✓	1.4b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 z a))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 8511 to 1738 computations (79.6% saved)

regimes523.0ms (10.5%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Counts

68 → 3

Compiler

Compiled 9235 to 5406 computations (41.5% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

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	25	86
1	33	86
2	40	86
3	44	86
4	46	86
5	45	86

end85.0ms (1.7%)

Compiler: Compiled 251 to 115 computations (54.2% saved)

Details

analyze1.2s (24.8%)

sample1.2s (23.9%)

simplify123.0ms (2.5%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series49.0ms (1%)

rewrite13.0ms (0.3%)

simplify86.0ms (1.7%)

prune112.0ms (2.2%)

localize8.0ms (0.2%)

series70.0ms (1.4%)

rewrite43.0ms (0.9%)

simplify188.0ms (3.8%)

prune273.0ms (5.5%)

localize8.0ms (0.2%)

series57.0ms (1.1%)

rewrite22.0ms (0.4%)

simplify138.0ms (2.8%)

prune181.0ms (3.6%)

localize10.0ms (0.2%)

series105.0ms (2.1%)

rewrite26.0ms (0.5%)

simplify217.0ms (4.3%)

prune206.0ms (4.1%)

regimes523.0ms (10.5%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end85.0ms (1.7%)

Profiling