Details

analyze201.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample1.4s (12.4%)

Results

1.3s	8256×	body	128	valid
2.0ms	12×	body	128	invalid

Compiler

Compiled 92 to 65 computations (29.3% saved)

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
592×	`fma-def_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	38
3	824	36
4	3882	36
5	5029	36

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 106 to 73 computations (31.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
✓	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.5b	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

series206.0ms (1.9%)

Counts

4 → 72

Calls

4 calls:

141.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
47.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
15.0ms	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
2.0ms	(*.f64 (PI.f64) t)

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

4 → 131

Calls

4 calls:

11.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
10.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
8.0ms	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
3.0ms	(*.f64 (PI.f64) t)

simplify147.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-r_binary64`
513×	`associate-l_binary64`
460×	`associate-/r*_binary64`
416×	`times-frac_binary64`
245×	`associate-/l*_binary64`

Counts

203 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	7617
1	1247	6841
2	5223	6841

prune348.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	6	226
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	6	227

Error

Counts

227 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 (sqrt.f64 (fma.f64 v (.f64 v -5) 1)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))
	0.8b	(-.f64 (fma.f64 3/4 (/.f64 (.f64 v v) (.f64 (.f64 (PI.f64) t) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t))) (.f64 4 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t)) (.f64 v v))))
	0.7b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))
▶	0.3b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
	1.1b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))

Compiler

Compiled 9519 to 5901 computations (38% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
	0.3b	(*.f64 (PI.f64) t)
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
✓	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))

series199.0ms (1.8%)

Counts

2 → 36

Calls

2 calls:

181.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

18.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

rewrite77.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

2 → 113

Calls

2 calls:

9.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

3.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

simplify191.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
419×	`associate-/r*_binary64`
279×	`times-frac_binary64`
276×	`associate-/l*_binary64`
250×	`associate-l_binary64`

Counts

149 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	7537
1	1236	6895
2	4807	6872
3	5527	6872

prune394.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	287	2	289
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	290	5	295

Error

Counts

295 → 5

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	0.4b	(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (/.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))))
▶	0.4b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	0.8b	(-.f64 (fma.f64 3/4 (/.f64 (.f64 v v) (.f64 (.f64 (PI.f64) t) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t))) (.f64 4 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t)) (.f64 v v))))
	0.7b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))

Compiler

Compiled 12149 to 7972 computations (34.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
✓	0.4b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))

series215.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

157.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
58.0ms	(/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
43×	`add-cbrt-cube_binary64`
28×	`div-exp_binary64`
27×	`add-sqr-sqrt_binary64`

Counts

2 → 114

Calls

2 calls:

16.0ms	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
8.0ms	(/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

simplify145.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
419×	`associate-/r*_binary64`
324×	`times-frac_binary64`
300×	`associate-l_binary64`
266×	`associate-r_binary64`

Counts

162 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	382	6855
1	1074	5963
2	4720	5938
3	5501	5938

prune404.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
▶	0.4b	(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (/.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))))
✓	0.4b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	0.8b	(-.f64 (fma.f64 3/4 (/.f64 (.f64 v v) (.f64 (.f64 (PI.f64) t) (sqrt.f64 1/2))) (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t))) (.f64 4 (.f64 (/.f64 (sqrt.f64 1/2) (.f64 (PI.f64) t)) (.f64 v v))))
	0.7b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))

Compiler

Compiled 12753 to 8507 computations (33.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (/.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))))
✓	0.4b	(/.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))))
✓	1.0b	(sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))))
	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))

series907.0ms (8.2%)

Counts

3 → 60

Calls

3 calls:

739.0ms

(/.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))))

147.0ms

(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))) (/.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))))

20.0ms

(sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))

rewrite498.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

2507×	`times-frac_binary64`
1861×	`sqrt-prod_binary64`
873×	`add-sqr-sqrt_binary64`
868×	`*-un-lft-identity_binary64`
868×	`add-cube-cbrt_binary64`

Counts

3 → 936

Calls

3 calls:

35.0ms

(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))) (/.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))))

11.0ms

(/.f64 (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))))

5.0ms

(sqrt.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))

simplify1.5s (13.5%)

Algorithm

1×	egg-herbie

Rules

623×	`times-frac_binary64`
581×	`associate-/r/_binary64`
461×	`fma-def_binary64`
185×	`*-commutative_binary64`
110×	`sub-neg_binary64`

Counts

996 → 1247

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1366	100404
1	3450	96610
2	5041	96610

prune2.7s (24.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	1493	1	1494
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	1494	5	1499

Error

Counts

1499 → 5

Alt Table

Status	Error	Program
	0.7b	(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (pow.f64 2 1/4) (.f64 (PI.f64) t)))
	0.7b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
✓	0.4b	(/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (/.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))))))
✓	0.4b	(.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 1 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	0.7b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (PI.f64) (*.f64 t (sqrt.f64 2))))

Compiler

Compiled 108007 to 77699 computations (28.1% saved)

regimes1.2s (10.9%)

Accuracy

Total 0.3b remaining (86.3%)

Threshold costs 0.3b (86.3%)

Counts

158 → 1

Compiler

Compiled 29641 to 21603 computations (27.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	37
1	31	37
2	40	37
3	49	37
4	55	37
5	58	37
6	59	37
7	58	37

end130.0ms (1.2%)

Compiler: Compiled 193 to 146 computations (24.4% saved)

Details

analyze201.0ms (1.8%)

sample1.4s (12.4%)

simplify33.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series206.0ms (1.9%)

rewrite44.0ms (0.4%)

simplify147.0ms (1.3%)

prune348.0ms (3.1%)

localize18.0ms (0.2%)

series199.0ms (1.8%)

rewrite77.0ms (0.7%)

simplify191.0ms (1.7%)

prune394.0ms (3.6%)

localize17.0ms (0.2%)

series215.0ms (1.9%)

rewrite40.0ms (0.4%)

simplify145.0ms (1.3%)

prune404.0ms (3.7%)

localize18.0ms (0.2%)

series907.0ms (8.2%)

rewrite498.0ms (4.5%)

simplify1.5s (13.5%)

prune2.7s (24.6%)

regimes1.2s (10.9%)

simplify5.0ms (0%)

end130.0ms (1.2%)

Profiling