Details

analyze915.0ms (14%)

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
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.6s (24.5%)

Results

1.0s	8256×	body	128	valid
352.0ms	3084×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

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

5.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.8b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
▶	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 95 to 57 computations (40% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	5.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series37.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

33.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
5.0ms	(-.f64 t (*.f64 z z))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-neg_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(-.f64 t (*.f64 z z))
0.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

703×	`distribute-rgt-in_binary64`
653×	`distribute-lft-in_binary64`
495×	`fma-neg_binary64`
369×	`exp-prod_binary64`
193×	`fma-def_binary64`

Counts

103 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1591
1	187	1301
2	431	1282
3	1535	1282
4	4588	1282
5	5085	1282

prune43.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

4.9b

Counts

66 → 5

Alt Table

Status	Error	Program
	40.1b	(pow.f64 x 2)
	36.9b	(.f64 4 (.f64 y t))
	22.4b	(.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	5.5b	(fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 1177 to 461 computations (60.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 z z))
✓	0.0b	(fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x))
✓	5.2b	(.f64 y (-.f64 t (.f64 z z)))

series47.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x))
15.0ms	(.f64 y (-.f64 t (.f64 z z)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(.f64 y (-.f64 t (.f64 z z)))
0.0ms	(fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

863×	`fma-def_binary64`
415×	`unsub-neg_binary64`
319×	`fma-neg_binary64`
311×	`exp-prod_binary64`
289×	`*-commutative_binary64`

Counts

127 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	2052
1	244	1730
2	681	1694
3	1807	1676
4	3479	1676
5	4944	1676
6	4867	1676

prune91.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	121	3	124

Error

0.0b

Counts

124 → 3

Alt Table

Status	Error	Program
▶	6.2b	(fma.f64 4 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (*.f64 x x))
	23.4b	(fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 2149 to 656 computations (69.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (*.f64 z z)))))
	5.2b	(.f64 y (-.f64 t (.f64 z z)))
✓	5.7b	(cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))

series990.0ms (15.2%)

Counts

3 → 108

Calls

3 calls:

535.0ms

(*.f64 (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))) (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))))

415.0ms

(cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z))))

39.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))) (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z))))) (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))) (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z))))) (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))) (cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z)))))

3.0ms

(cbrt.f64 (*.f64 y (-.f64 t (*.f64 z z))))

simplify161.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

352×	`associate-r_binary64`
296×	`associate-l_binary64`
246×	`sub-neg_binary64`
229×	`*-commutative_binary64`
213×	`times-frac_binary64`

Counts

223 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	446	7545
1	1186	7022
2	4242	6620
3	5077	6620

prune671.0ms (10.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	587	0	587
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	587	3	590

Error

0.0b

Counts

590 → 3

Alt Table

Status	Error	Program
✓	6.2b	(fma.f64 4 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (*.f64 x x))
▶	23.4b	(fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 27038 to 8609 computations (68.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))
✓	0.2b	(.f64 z (.f64 y -4))

series25.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

21.0ms	(fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))
4.0ms	(.f64 z (.f64 y -4))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 z (.f64 y -4))
0.0ms	(fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-l_binary64`
433×	`unsub-neg_binary64`
360×	`distribute-rgt-neg-in_binary64`
353×	`associate-r_binary64`
308×	`fma-neg_binary64`

Counts

90 → 54

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	1078
1	127	959
2	372	959
3	1269	959
4	2700	959
5	4507	959
6	4911	959

prune34.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	53	4	57

Error

0.0b

Counts

57 → 4

Alt Table

Status	Error	Program
✓	6.2b	(fma.f64 4 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (*.f64 x x))
	24.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 z (.f64 y -4)) (.f64 x x))) (cbrt.f64 (fma.f64 z (.f64 z (.f64 y -4)) (.f64 x x)))) (cbrt.f64 (fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))))
✓	23.4b	(fma.f64 z (.f64 z (.f64 y -4)) (*.f64 x x))
✓	5.8b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 894 to 411 computations (54% saved)

regimes1.4s (21.9%)

Accuracy

Total 0.4b remaining (91.1%)

Threshold costs 0.4b (91.1%)

Counts

86 → 2

Compiler

Compiled 18178 to 11334 computations (37.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	27	40
2	34	40
3	38	40
4	40	40
5	40	40

end76.0ms (1.2%)

Compiler: Compiled 168 to 88 computations (47.6% saved)

Details

analyze915.0ms (14%)

sample1.6s (24.5%)

simplify66.0ms (1%)

prune3.0ms (0.1%)

localize9.0ms (0.1%)

series37.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify74.0ms (1.1%)

prune43.0ms (0.7%)

localize9.0ms (0.1%)

series47.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify100.0ms (1.5%)

prune91.0ms (1.4%)

localize11.0ms (0.2%)

series990.0ms (15.2%)

rewrite35.0ms (0.5%)

simplify161.0ms (2.5%)

prune671.0ms (10.3%)

localize6.0ms (0.1%)

series25.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify70.0ms (1.1%)

prune34.0ms (0.5%)

regimes1.4s (21.9%)

bsearch3.0ms (0%)

simplify3.0ms (0.1%)

end76.0ms (1.2%)

Profiling