Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 27 to 22 computations (18.5% saved)

sample2.1s (70.8%)

Results

1.8s

8256×

body

256

valid

Compiler

Compiled 74 to 61 computations (17.6% saved)

simplify170.0ms (5.6%)

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)

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite9.0ms (0.3%)

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:

5.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
3.0ms	(*.f64 t 1/25000000000000000000000000000000)

simplify74.0ms (2.4%)

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

prune40.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	57	5	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	6	63

Error

Counts

63 → 6

Alt Table

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

Compiler

Compiled 689 to 449 computations (34.8% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`unswap-sqr_binary64`
397×	`log-prod_binary64`
394×	`sqr-pow_binary64`
337×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	303
1	98	231
2	199	221
3	637	215
4	1073	215
5	2846	215
6	3959	215
7	4849	215
8	4882	215

prune32.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	45	6	51

Error

Counts

51 → 6

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (sqrt.f64 1/25000000000000000000000000000000) (.f64 t (*.f64 t 1/5000000000000000)))
	0.5b	(.f64 (sqrt.f64 1/25000000000000000000000000000000) (.f64 (sqrt.f64 1/25000000000000000000000000000000) (pow.f64 t 2)))
	0.5b	(.f64 (sqrt.f64 t) (.f64 1/25000000000000000000000000000000 (pow.f64 t 3/2)))
✓	0.4b	(.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 543 to 417 computations (23.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 t 1/5000000000000000)
✓	0.2b	(.f64 t (.f64 t 1/5000000000000000))
✓	0.3b	(.f64 (sqrt.f64 1/25000000000000000000000000000000) (.f64 t (*.f64 t 1/5000000000000000)))

series7.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 (sqrt.f64 1/25000000000000000000000000000000) (.f64 t (*.f64 t 1/5000000000000000)))
2.0ms	(.f64 t (.f64 t 1/5000000000000000))
2.0ms	(*.f64 t 1/5000000000000000)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
19×	`pow1_binary64`
12×	`associate-l_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

3 → 66

Calls

3 calls:

9.0ms	(.f64 (sqrt.f64 1/25000000000000000000000000000000) (.f64 t (*.f64 t 1/5000000000000000)))
3.0ms	(.f64 t (.f64 t 1/5000000000000000))
3.0ms	(*.f64 t 1/5000000000000000)

simplify80.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-def_binary64`
506×	`associate-*l/_binary64`
482×	`unswap-sqr_binary64`
318×	`associate-/l/_binary64`
266×	`associate-/r/_binary64`

Counts

102 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	857
1	159	749
2	557	728
3	789	726
4	1141	726
5	1781	726
6	4938	726
7	5110	726

prune53.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	88	6	94

Error

Counts

94 → 6

Alt Table

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

Compiler

Compiled 1196 to 873 computations (27% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(*.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)))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))
1.0ms	(.f64 (.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))

rewrite15.0ms (0.5%)

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:

7.0ms	(.f64 (.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000))
5.0ms	(.f64 t (.f64 (*.f64 t 1/5000000000000000) (sqrt.f64 1/25000000000000000000000000000000)))

simplify61.0ms (2%)

Algorithm

1×	egg-herbie

Rules

649×	`unswap-sqr_binary64`
338×	`associate-+l+_binary64`
276×	`*-commutative_binary64`
268×	`associate-*r/_binary64`
267×	`fma-def_binary64`

Counts

70 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	581
1	154	482
2	528	470
3	797	460
4	1147	460
5	1776	460
6	4885	460

prune56.0ms (1.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	89	6	95

Error

Counts

95 → 6

Alt Table

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

Compiler

Compiled 1142 to 851 computations (25.5% saved)

regimes85.0ms (2.8%)

Accuracy

Total 0.4b remaining (98.5%)

Threshold costs 0.4b (98.5%)

Counts

29 → 1

Compiler

Compiled 1018 to 774 computations (24% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7
2	7	7

end66.0ms (2.2%)

Compiler: Compiled 60 to 46 computations (23.3% saved)

Details

analyze1.0ms (0%)

sample2.1s (70.8%)

simplify170.0ms (5.6%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite9.0ms (0.3%)

simplify74.0ms (2.4%)

prune40.0ms (1.3%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify75.0ms (2.5%)

prune32.0ms (1.1%)

localize5.0ms (0.2%)

series7.0ms (0.2%)

rewrite18.0ms (0.6%)

simplify80.0ms (2.6%)

prune53.0ms (1.8%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite15.0ms (0.5%)

simplify61.0ms (2%)

prune56.0ms (1.9%)

regimes85.0ms (2.8%)

simplify2.0ms (0.1%)

end66.0ms (2.2%)

Profiling