Details

analyze1.2s (27.9%)

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)

sample1.2s (25.9%)

Results

985.0ms	8256×	body	128	valid
102.0ms	818×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify111.0ms (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
	11.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series57.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

38.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
20.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite10.0ms (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)

simplify89.0ms (2%)

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

prune92.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	6	137

Error

0.0b

Counts

137 → 6

Alt Table

Status	Error	Program
▶	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
	11.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	42.5b	(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)))
	28.6b	(fma.f64 (/.f64 y a) t x)
	17.2b	(fma.f64 y (-.f64 1 (/.f64 t z)) x)
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 3390 to 1103 computations (67.5% saved)

localize9.0ms (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)
✓	5.9b	(/.f64 (*.f64 y t) (-.f64 z a))

series116.0ms (2.6%)

Counts

4 → 156

Calls

4 calls:

54.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
26.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
20.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)
15.0ms	(/.f64 y (-.f64 z a))

rewrite32.0ms (0.7%)

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:

8.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
7.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
3.0ms	(/.f64 y (-.f64 z a))
0.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)

simplify209.0ms (4.7%)

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

prune171.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	264	1	265
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	266	5	271

Error

Counts

271 → 5

Alt Table

Status	Error	Program
▶	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (.f64 (.f64 y t) (/.f64 1 (-.f64 z a))))
	11.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
	28.6b	(fma.f64 (/.f64 y a) t x)
	17.2b	(fma.f64 y (-.f64 1 (/.f64 t z)) x)
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 8529 to 1758 computations (79.4% saved)

localize10.0ms (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 1 (-.f64 z a))))
✓	0.0b	(/.f64 1 (-.f64 z a))
	2.5b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	6.0b	(.f64 (.f64 y t) (/.f64 1 (-.f64 z a)))

series84.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

47.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (.f64 (.f64 y t) (/.f64 1 (-.f64 z a))))
28.0ms	(.f64 (.f64 y t) (/.f64 1 (-.f64 z a)))
8.0ms	(/.f64 1 (-.f64 z a))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
29×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 112

Calls

3 calls:

9.0ms	(.f64 (.f64 y t) (/.f64 1 (-.f64 z a)))
4.0ms	(/.f64 1 (-.f64 z a))
3.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (.f64 (.f64 y t) (/.f64 1 (-.f64 z a))))

simplify133.0ms (3%)

Algorithm

1×	egg-herbie

Rules

519×	`cancel-sign-sub-inv_binary64`
367×	`fma-neg_binary64`
253×	`neg-mul-1_binary64`
232×	`distribute-rgt-neg-in_binary64`
217×	`distribute-rgt-in_binary64`

Counts

244 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	5104
1	696	4914
2	2512	4158
3	4530	4154
4	5028	4154

prune155.0ms (3.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	256	5	261

Error

Counts

261 → 5

Alt Table

Status	Error	Program
✓	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (.f64 (.f64 y t) (/.f64 1 (-.f64 z a))))
	11.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
▶	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	17.2b	(fma.f64 y (-.f64 1 (/.f64 t z)) x)
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 6951 to 2096 computations (69.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 z a))
✓	10.2b	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

series31.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

30.0ms

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

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`
21×	`associate-l_binary64`
18×	`prod-diff_binary64`

Counts

1 → 74

Calls

1 calls:

10.0ms

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

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
397×	`distribute-rgt-in_binary64`
317×	`cancel-sign-sub-inv_binary64`
308×	`fma-neg_binary64`
188×	`associate-r_binary64`

Counts

122 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	3067
1	635	2947
2	2366	2624
3	4992	2624
4	5097	2624

prune128.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	197	5	202

Error

Counts

202 → 5

Alt Table

Status	Error	Program
✓	7.3b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (.f64 (.f64 y t) (/.f64 1 (-.f64 z a))))
	11.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	17.2b	(fma.f64 y (-.f64 1 (/.f64 t z)) x)
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Compiler

Compiled 4849 to 1414 computations (70.8% saved)

regimes383.0ms (8.6%)

Accuracy

Total 1.3b remaining (98.8%)

Threshold costs 0b (0%)

Counts

63 → 1

Compiler

Compiled 7597 to 4643 computations (38.9% saved)

simplify2.0ms (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	10	14
1	14	14
2	22	14
3	26	14
4	28	14
5	28	14

end67.0ms (1.5%)

Compiler: Compiled 113 to 69 computations (38.9% saved)

Details

analyze1.2s (27.9%)

sample1.2s (25.9%)

simplify111.0ms (2.5%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series57.0ms (1.3%)

rewrite10.0ms (0.2%)

simplify89.0ms (2%)

prune92.0ms (2.1%)

localize9.0ms (0.2%)

series116.0ms (2.6%)

rewrite32.0ms (0.7%)

simplify209.0ms (4.7%)

prune171.0ms (3.8%)

localize10.0ms (0.2%)

series84.0ms (1.9%)

rewrite22.0ms (0.5%)

simplify133.0ms (3%)

prune155.0ms (3.5%)

localize8.0ms (0.2%)

series31.0ms (0.7%)

rewrite16.0ms (0.4%)

simplify103.0ms (2.3%)

prune128.0ms (2.9%)

regimes383.0ms (8.6%)

simplify2.0ms (0%)

end67.0ms (1.5%)

Profiling