Details

analyze139.0ms (2.7%)

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)

sample60.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify30.0ms (0.6%)

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 (0.1%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (.f64 (.f64 (.f64 (PI.f64) t) (sqrt.f64 (.f64 2 (-.f64 1 (.f64 3 (.f64 v v)))))) (-.f64 1 (*.f64 v v))))
▶	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)))))

Status

Error

Program

0.3b

(/.f64 (-.f64 1 (*.f64 5 (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 2 (-.f64 1 (*.f64 3 (*.f64 v v)))))) (-.f64 1 (*.f64 v v))))

▶

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)))))

Compiler

Compiled 166 to 115 computations (30.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series185.0ms (3.6%)

Counts

4 → 60

Calls

4 calls:

132.0ms	(/.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)))))
43.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
7.0ms	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))
2.0ms	(*.f64 (PI.f64) t)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-cbrt-cube_binary64`
29×	`add-exp-log_binary64`
20×	`distribute-lft-in_binary64`
20×	`distribute-rgt-in_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

4 → 112

Calls

4 calls:

9.0ms	(/.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)))))
8.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
3.0ms	(*.f64 (PI.f64) t)
1.0ms	(sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))

simplify138.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary64`
492×	`associate-l_binary64`
482×	`associate-/r*_binary64`
433×	`times-frac_binary64`
256×	`associate-/l*_binary64`

Counts

172 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	7020
1	1319	6443
2	4898	6428
3	5385	6428

prune262.0ms (5.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	226	5	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	228	5	233

Error

0.0b

Counts

233 → 5

Alt Table

Status	Error	Program
▶	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))))
	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))))))
	1.2b	(-.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))))
	0.4b	(.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)))))
	1.0b	(/.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))))))

Compiler

Compiled 9703 to 6199 computations (36.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series143.0ms (2.8%)

Counts

2 → 36

Calls

2 calls:

130.0ms

(/.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))))

13.0ms

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

rewrite25.0ms (0.5%)

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)))

simplify150.0ms (2.9%)

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

prune309.0ms (6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	286	2	288
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	287	6	293

Error

Counts

293 → 6

Alt Table

Status	Error	Program
	0.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (PI.f64) t)) (/.f64 (sqrt.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (-.f64 1 (*.f64 v v))))
▶	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 -6 v) 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))))
	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))))))
	1.2b	(-.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))))
	1.0b	(/.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))))))

Compiler

Compiled 12262 to 8216 computations (33% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series179.0ms (3.5%)

Counts

2 → 48

Calls

2 calls:

136.0ms

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

44.0ms

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

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
12×	`cbrt-unprod_binary64`
12×	`prod-exp_binary64`
11×	`pow1_binary64`

Counts

2 → 57

Calls

2 calls:

11.0ms

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

8.0ms

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

simplify113.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
401×	`associate-l_binary64`
391×	`associate-/r*_binary64`
374×	`associate-r_binary64`
333×	`times-frac_binary64`

Counts

105 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	5364
1	1149	4796
2	4708	4771
3	5473	4771

prune215.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	208	5	213

Error

Counts

213 → 5

Alt Table

Status	Error	Program
✓	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))))
▶	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))
	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))))))
	1.2b	(-.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))))
	1.0b	(/.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))))))

Compiler

Compiled 8566 to 5558 computations (35.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series192.0ms (3.7%)

Counts

2 → 48

Calls

2 calls:

129.0ms

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

63.0ms

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

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 117

Calls

2 calls:

9.0ms

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

6.0ms

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

simplify190.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

415×	`associate-/r*_binary64`
311×	`associate-r_binary64`
311×	`times-frac_binary64`
242×	`associate-l_binary64`
212×	`associate-/l*_binary64`

Counts

165 → 214

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	418	8593
1	1155	7965
2	4791	7965
3	4999	7965
4	4938	7965

prune273.0ms (5.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	282	5	287

Error

Counts

287 → 5

Alt Table

Status	Error	Program
✓	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))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))
	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))))))
	1.2b	(-.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))))
	1.0b	(/.f64 (/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (fabs.f64 (cbrt.f64 (fma.f64 v (.f64 v -6) 2)))) (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))))

Compiler

Compiled 11635 to 7483 computations (35.7% saved)

regimes1.4s (27.9%)

Accuracy

Total 0.3b remaining (85.7%)

Threshold costs 0.3b (85.7%)

Counts

179 → 1

Compiler

Compiled 32518 to 23944 computations (26.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	39	53
2	59	53
3	71	53
4	80	53
5	83	53
6	81	53

end1.0ms (0%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

sample972.0ms (18.8%)

Algorithm

1×

intervals

Results

651.0ms	8000×	body	128	valid
1.0ms	9×	body	128	nan

Compiler

Compiled 220 to 164 computations (25.5% saved)

Details

analyze139.0ms (2.7%)

sample60.0ms (1.2%)

simplify30.0ms (0.6%)

prune4.0ms (0.1%)

localize15.0ms (0.3%)

series185.0ms (3.6%)

rewrite28.0ms (0.5%)

simplify138.0ms (2.7%)

prune262.0ms (5.1%)

localize15.0ms (0.3%)

series143.0ms (2.8%)

rewrite25.0ms (0.5%)

simplify150.0ms (2.9%)

prune309.0ms (6%)

localize16.0ms (0.3%)

series179.0ms (3.5%)

rewrite24.0ms (0.5%)

simplify113.0ms (2.2%)

prune215.0ms (4.2%)

localize14.0ms (0.3%)

series192.0ms (3.7%)

rewrite30.0ms (0.6%)

simplify190.0ms (3.7%)

prune273.0ms (5.3%)

regimes1.4s (27.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample972.0ms (18.8%)

Profiling