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)

sample2.2s (65.4%)

Results

2.0s

8256×

body

256

valid

Compiler

Compiled 74 to 61 computations (17.6% saved)

simplify170.0ms (5.1%)

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:

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

rewrite77.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

760×	`log1p-udef_binary64`
414×	`log1p-expm1-u_binary64`
414×	`expm1-log1p-u_binary64`
352×	`pow1_binary64`
308×	`unpow-prod-down_binary64`

Counts

2 → 42

Calls

2 calls:

77.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))
77.0ms	(*.f64 t 1/25000000000000000000000000000000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	102	11
2	1113	11
3	4782	11
4	5985	11
0	0	0
1	0	0

simplify155.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

66 → 45

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	132
1	14	132
2	22	132
3	41	132
4	88	132
5	221	132
6	693	132
7	1098	132
8	1100	132
9	1248	132
10	1418	132
11	1600	132
12	1825	132
13	2110	132
14	2529	132
15	3094	132
16	3780	132
17	3998	132
18	4242	132
19	4324	132
20	4357	132
21	4378	132
22	4947	132

prune27.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	40	5	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	6	46

Error

0.0b

Counts

46 → 6

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.4b	(.f64 t (sqrt.f64 (.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))
	0.7b	(.f64 t (pow.f64 (.f64 (sqrt.f64 t) 1/5000000000000000) 2))
	1.9b	(.f64 t (pow.f64 (cbrt.f64 (.f64 t 1/25000000000000000000000000000000)) 3))
▶	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

Compiler

Compiled 466 to 344 computations (26.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

9.0ms

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

rewrite80.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

821×	`log1p-udef_binary64`
445×	`log1p-expm1-u_binary64`
445×	`expm1-log1p-u_binary64`
270×	`unpow-prod-down_binary64`
222×	`log-prod_binary64`

Counts

1 → 22

Calls

1 calls:

79.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	124	7
2	1187	7
3	4830	7
4	6088	7
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune16.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	22	6	28

Error

Counts

28 → 6

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
	0.4b	(.f64 t (sqrt.f64 (.f64 (*.f64 t t) 1/625000000000000000000000000000000000000000000000000000000000000)))
	1.9b	(.f64 t (pow.f64 (cbrt.f64 (.f64 t 1/25000000000000000000000000000000)) 3))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
▶	0.3b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))

Compiler

Compiled 261 to 187 computations (28.4% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))
✓	0.3b	(*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4))

series5.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4))
2.0ms	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))

rewrite47.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`log1p-expm1-u_binary64`
539×	`expm1-log1p-u_binary64`
447×	`unpow-prod-down_binary64`
275×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

2 → 71

Calls

2 calls:

45.0ms	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))
45.0ms	(*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	14
2	1446	14
3	5160	14
0	0	0
1	0	0

simplify153.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

83 → 72

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	22	84
3	41	84
4	88	84
5	221	84
6	693	84
7	1098	84
8	1100	84
9	1248	84
10	1418	84
11	1600	84
12	1825	84
13	2110	84
14	2529	84
15	3094	84
16	3780	84
17	3998	84
18	4242	84
19	4324	84
20	4357	84
21	4378	84
22	4947	84

prune40.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	74	4	78

Error

Counts

78 → 4

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
▶	0.6b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
✓	0.3b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))

Compiler

Compiled 809 to 588 computations (27.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
✓	1.0b	(pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2)

series3.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
0.0ms	(pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2)

rewrite42.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

526×	`log1p-expm1-u_binary64`
526×	`expm1-log1p-u_binary64`
305×	`unpow-prod-down_binary64`
255×	`log-prod_binary64`
158×	`pow2_binary64`

Counts

2 → 19

Calls

2 calls:

42.0ms	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
42.0ms	(pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	149	8
2	1394	8
3	4852	8
0	0	0
1	0	0

simplify164.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1108×	`sqr-pow_binary64`
573×	`fabs-mul_binary64`
560×	`cube-prod_binary64`
536×	`pow-sqr_binary64`
454×	`associate-l_binary64`

Counts

31 → 20

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	22	84
3	41	84
4	88	84
5	221	84
6	693	84
7	1098	84
8	1100	84
9	1248	84
10	1418	84
11	1600	84
12	1825	84
13	2110	84
14	2529	84
15	3094	84
16	3780	84
17	3998	84
18	4242	84
19	4324	84
20	4357	84
21	4378	84
22	4947	84

prune9.0ms (0.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	20	4	24

Error

Counts

24 → 4

Alt Table

Status	Error	Program
✓	0.4b	(.f64 t (.f64 t 1/25000000000000000000000000000000))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
✓	0.6b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
✓	0.3b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))

Compiler

Compiled 191 to 128 computations (33% saved)

regimes64.0ms (1.9%)

Accuracy

Total 0.2b remaining (98.9%)

Threshold costs 0.2b (98.9%)

Counts

17 → 1

Compiler

Compiled 537 to 431 computations (19.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
2	8	9

end56.0ms (1.7%)

Compiler: Compiled 41 to 33 computations (19.5% saved)

Details

analyze1.0ms (0%)

sample2.2s (65.4%)

simplify170.0ms (5.1%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite77.0ms (2.3%)

simplify155.0ms (4.7%)

prune27.0ms (0.8%)

localize3.0ms (0.1%)

series9.0ms (0.3%)

rewrite80.0ms (2.4%)

simplify6.0ms (0.2%)

prune16.0ms (0.5%)

localize4.0ms (0.1%)

series5.0ms (0.2%)

rewrite47.0ms (1.4%)

simplify153.0ms (4.6%)

prune40.0ms (1.2%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite42.0ms (1.3%)

simplify164.0ms (4.9%)

prune9.0ms (0.3%)

regimes64.0ms (1.9%)

simplify2.0ms (0.1%)

end56.0ms (1.7%)

Profiling