Details

analyze182.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 27 to 22 computations (18.5% saved)

sample45.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	256	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 48 to 40 computations (16.7% saved)

simplify167.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
760×	`unsub-neg_binary64`
633×	`distribute-neg-in_binary64`
628×	`distribute-rgt-neg-in_binary64`
564×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	35	19
2	98	17
3	302	15
4	923	7
5	2332	7
6	3226	7
7	3864	7
8	4544	7
9	4793	7
10	4822	7
11	4798	7
12	4830	7
13	4680	7
14	4874	7
15	4821	7

prune4.0ms (0.1%)

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 t (.f64 t 1/25000000000000000000000000000000))

Compiler

Compiled 37 to 28 computations (24.3% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.4b	(*.f64 t 1/25000000000000000000000000000000)

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
2.0ms	(*.f64 t 1/25000000000000000000000000000000)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 40

Calls

2 calls:

4.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
3.0ms	(*.f64 t 1/25000000000000000000000000000000)

simplify91.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

970×	`fma-def_binary64`
331×	`associate-l_binary64`
261×	`associate-*r/_binary64`
229×	`associate-*l/_binary64`
217×	`*-commutative_binary64`

Counts

64 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	478
1	112	430
2	327	421
3	594	419
4	851	419
5	1427	419
6	3364	419
7	4801	419
8	4930	419

prune49.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	53	9	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	10	63

Error

0.0b

Counts

63 → 10

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.6b	(.f64 (sqrt.f64 t) (.f64 (sqrt.f64 t) (*.f64 t 1/25000000000000000000000000000000)))
	0.6b	(.f64 t (cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 1/25000000000000000000000000000000 1/25000000000000000000000000000000) 1/25000000000000000000000000000000))))
	0.7b	(.f64 t (.f64 (.f64 (sqrt.f64 t) 1/5000000000000000) (.f64 (sqrt.f64 t) 1/5000000000000000)))
	0.5b	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))
	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))
	0.7b	(cbrt.f64 (*.f64 1/15625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 6)))
	0.7b	(cbrt.f64 (.f64 (.f64 (.f64 t (.f64 t 1/25000000000000000000000000000000)) (.f64 t (.f64 t 1/25000000000000000000000000000000))) (.f64 t (.f64 t 1/25000000000000000000000000000000))))
	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
▶	0.4b	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

Compiler

Compiled 801 to 525 computations (34.5% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 t 1/5000000000000000)
✓	0.2b	(.f64 (.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))
✓	0.3b	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

series14.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

10.0ms

(*.f64 t (*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

2.0ms

(*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))

2.0ms

(*.f64 t 1/5000000000000000)

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
10×	`associate-r_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 66

Calls

3 calls:

6.0ms

(*.f64 t (*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

5.0ms

(*.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))

3.0ms

(*.f64 t 1/5000000000000000)

simplify82.0ms (2%)

Algorithm

1×	egg-herbie

Rules

649×	`unswap-sqr_binary64`
623×	`fma-def_binary64`
280×	`*-commutative_binary64`
272×	`associate-*r/_binary64`
234×	`associate-*l/_binary64`

Counts

102 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	751
1	174	652
2	571	640
3	854	638
4	1191	638
5	1833	638
6	4792	638
7	4941	638

prune58.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	6	2	8
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Error

Counts

98 → 5

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.5b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))
	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))
▶	0.4b	(.f64 (.f64 t (*.f64 t 1/5000000000000000)) (sqrt.f64 1/25000000000000000000000000000000))

Compiler

Compiled 1176 to 874 computations (25.7% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.2b	(*.f64 t 1/5000000000000000)
✓	0.2b	(.f64 t (.f64 t 1/5000000000000000))
✓	0.3b	(.f64 (.f64 t (*.f64 t 1/5000000000000000)) (sqrt.f64 1/25000000000000000000000000000000))

series15.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

12.0ms	(.f64 (.f64 t (*.f64 t 1/5000000000000000)) (sqrt.f64 1/25000000000000000000000000000000))
3.0ms	(.f64 t (.f64 t 1/5000000000000000))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 46

Calls

2 calls:

6.0ms	(.f64 (.f64 t (*.f64 t 1/5000000000000000)) (sqrt.f64 1/25000000000000000000000000000000))
4.0ms	(.f64 t (.f64 t 1/5000000000000000))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

505×	`unswap-sqr_binary64`
326×	`associate-*r/_binary64`
325×	`associate-+l+_binary64`
294×	`associate-*l/_binary64`
271×	`fma-def_binary64`

Counts

70 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	682
1	152	580
2	539	559
3	768	553
4	1067	553
5	1694	553
6	4862	553

prune63.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	88	5	93

Error

Counts

93 → 5

Alt Table

Status	Error	Program
▶	0.5b	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.5b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))
	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))
✓	0.4b	(.f64 (.f64 t (*.f64 t 1/5000000000000000)) (sqrt.f64 1/25000000000000000000000000000000))

Compiler

Compiled 1198 to 870 computations (27.4% saved)

localize19.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2))

series16.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

9.0ms	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2))
6.0ms	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`prod-exp_binary64`
9×	`associate-l_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

7.0ms	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2))
6.0ms	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))

simplify92.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-def_binary64`
633×	`associate-l_binary64`
570×	`associate-r_binary64`
216×	`unswap-sqr_binary64`
214×	`log-div_binary64`

Counts

59 → 70

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	84	674
1	167	635
2	453	635
3	1742	555
4	2400	531
5	4024	501
6	4825	501
7	5007	501

prune46.0ms (1.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	70	5	75

Error

Counts

75 → 5

Alt Table

Status	Error	Program
✓	0.5b	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.5b	(.f64 t (.f64 t (*.f64 1/5000000000000000 (sqrt.f64 1/25000000000000000000000000000000))))
	0.6b	(cbrt.f64 (.f64 (.f64 (.f64 t t) t) (.f64 (.f64 (.f64 t 1/25000000000000000000000000000000) (.f64 t 1/25000000000000000000000000000000)) (.f64 t 1/25000000000000000000000000000000))))
✓	0.4b	(.f64 (.f64 t (*.f64 t 1/5000000000000000)) (sqrt.f64 1/25000000000000000000000000000000))

Compiler

Compiled 965 to 647 computations (33% saved)

regimes105.0ms (2.6%)

Accuracy

Total 0.4b remaining (98.3%)

Threshold costs 0.4b (98.3%)

Counts

38 → 1

Compiler

Compiled 1324 to 981 computations (25.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	10	10

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample2.8s (70.6%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	256	valid
380.0ms	8000×	pre	128	true

Compiler

Compiled 88 to 67 computations (23.9% saved)

Details

analyze182.0ms (4.6%)

sample45.0ms (1.1%)

simplify167.0ms (4.2%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite8.0ms (0.2%)

simplify91.0ms (2.3%)

prune49.0ms (1.2%)

localize5.0ms (0.1%)

series14.0ms (0.3%)

rewrite16.0ms (0.4%)

simplify82.0ms (2%)

prune58.0ms (1.5%)

localize5.0ms (0.1%)

series15.0ms (0.4%)

rewrite12.0ms (0.3%)

simplify57.0ms (1.4%)

prune63.0ms (1.6%)

localize19.0ms (0.5%)

series16.0ms (0.4%)

rewrite15.0ms (0.4%)

simplify92.0ms (2.3%)

prune46.0ms (1.1%)

regimes105.0ms (2.6%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.8s (70.6%)

Profiling