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)

sample1.8s (72.5%)

Results

1.8s

8256×

body

256

valid

Compiler

Compiled 54 to 44 computations (18.5% saved)

preprocess32.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

955×	`fma-def_binary64`
377×	`sub-neg_binary64`
267×	`distribute-neg-in_binary64`
151×	`associate-+l-_binary64`
151×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	35	19
2	115	17
3	354	15
4	1273	7
5	3641	7
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 17 computations (15% saved)

simplify22.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-def_binary64`
377×	`sub-neg_binary64`
267×	`distribute-neg-in_binary64`
151×	`associate-+l-_binary64`
151×	`associate--r+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	35	19
2	115	17
3	354	15
4	1273	7
5	3641	7

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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 (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))	t	-inf
1.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))	t	inf
1.0ms	(.f64 t (.f64 t 1/25000000000000000000000000000000))	t	0
0.0ms	(*.f64 t 1/25000000000000000000000000000000)	t	0
0.0ms	(*.f64 t 1/25000000000000000000000000000000)	t	inf

rewrite34.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

414×	`log1p-expm1-u_binary64`
414×	`expm1-log1p-u_binary64`
352×	`pow1_binary64`
308×	`unpow-prod-down_binary64`
239×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	102	11
2	1151	11

Stop Event

1×	node limit

Counts

2 → 40

simplify62.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
441×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	132
1	14	132
2	23	132
3	42	132
4	105	132
5	315	132
6	1204	132
7	2080	132
8	2244	132
9	2428	132
10	2636	132
11	2925	132
12	3318	132
13	3796	132
14	4359	132

Stop Event

1×	node limit

Counts

64 → 43

prune32.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	5	44

Error

0.0b

Counts

44 → 5

Alt Table

Status	Error	Program
	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
	4.4b	(exp.f64 (.f64 2 (log.f64 (.f64 t 1/5000000000000000))))
▶	0.2b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))
	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
	0.6b	(.f64 t (cbrt.f64 (pow.f64 (.f64 t 1/25000000000000000000000000000000) 3)))

Compiler

Compiled 444 to 348 computations (21.6% saved)

localize4.0ms (0.2%)

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

6 calls:

1.0ms	(*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4))	t	0
1.0ms	(*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4))	t	-inf
1.0ms	(*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4))	t	inf
1.0ms	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))	t	-inf
1.0ms	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))	t	inf

rewrite40.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	148	14
2	1558	14

Stop Event

1×	node limit

Counts

2 → 70

simplify58.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

607×	`sqr-pow_binary64`
445×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	107	84
5	336	84
6	1237	84
7	2113	84
8	2277	84
9	2461	84
10	2669	84
11	2960	84
12	3353	84
13	3833	84
14	4396	84

Stop Event

1×	node limit

Counts

82 → 71

prune43.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Error

Counts

76 → 5

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
✓	0.2b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))
	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
	0.6b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
	0.6b	(.f64 t (cbrt.f64 (pow.f64 (.f64 t 1/25000000000000000000000000000000) 3)))

Compiler

Compiled 833 to 636 computations (23.6% 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))

series2.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

1.0ms	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))	t	0
1.0ms	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))	t	-inf
1.0ms	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))	t	inf

rewrite29.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

445×	`log1p-expm1-u_binary64`
445×	`expm1-log1p-u_binary64`
271×	`unpow-prod-down_binary64`
222×	`log-prod_binary64`
135×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	124	7
2	1282	7

Stop Event

1×	node limit

Counts

1 → 20

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

20 → 20

prune11.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	20	5	25

Error

Counts

25 → 5

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
✓	0.2b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))
▶	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
	0.6b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))
	0.6b	(.f64 t (cbrt.f64 (pow.f64 (.f64 t 1/25000000000000000000000000000000) 3)))

Compiler

Compiled 230 to 176 computations (23.5% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 t 1/5000000000000000)
✓	0.4b	(pow.f64 (*.f64 t 1/5000000000000000) 2)

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(pow.f64 (*.f64 t 1/5000000000000000) 2)	t	0
1.0ms	(pow.f64 (*.f64 t 1/5000000000000000) 2)	t	inf
1.0ms	(pow.f64 (*.f64 t 1/5000000000000000) 2)	t	-inf
0.0ms	(*.f64 t 1/5000000000000000)	t	-inf
0.0ms	(*.f64 t 1/5000000000000000)	t	inf

rewrite34.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

453×	`log1p-expm1-u_binary64`
453×	`expm1-log1p-u_binary64`
314×	`unpow-prod-down_binary64`
232×	`log-prod_binary64`
136×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	126	11
2	1304	11

Stop Event

1×	node limit

Counts

2 → 60

simplify65.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

628×	`sqr-pow_binary64`
502×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
276×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	132
1	15	132
2	26	132
3	51	132
4	125	132
5	361	132
6	1340	132
7	2220	132
8	2384	132
9	2598	132
10	2818	132
11	3116	132
12	3518	132
13	4004	132
14	4563	132

Stop Event

1×	node limit

Counts

84 → 63

prune31.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	63	5	68

Error

Counts

68 → 5

Alt Table

Status	Error	Program
	0.4b	(.f64 1/5000000000000000 (.f64 t (*.f64 t 1/5000000000000000)))
✓	0.4b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))
✓	0.2b	(sqrt.f64 (*.f64 1/625000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 4)))
✓	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
	0.6b	(.f64 t (cbrt.f64 (pow.f64 (.f64 t 1/25000000000000000000000000000000) 3)))

Compiler

Compiled 629 to 487 computations (22.6% saved)

regimes77.0ms (3.1%)

Accuracy

Total 0.2b remaining (95.4%)

Threshold costs 0.2b (95.4%)

Counts

23 → 1

Compiler

Compiled 693 to 565 computations (18.5% 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

Stop Event

1×

saturated

end66.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 50 to 41 computations (18% saved)

Details

analyze1.0ms (0%)

sample1.8s (72.5%)

preprocess32.0ms (1.3%)

simplify22.0ms (0.9%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite34.0ms (1.4%)

simplify62.0ms (2.5%)

prune32.0ms (1.3%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite40.0ms (1.6%)

simplify58.0ms (2.3%)

prune43.0ms (1.7%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite29.0ms (1.2%)

simplify5.0ms (0.2%)

prune11.0ms (0.4%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite34.0ms (1.4%)

simplify65.0ms (2.7%)

prune31.0ms (1.3%)

regimes77.0ms (3.1%)

simplify2.0ms (0.1%)

end66.0ms (2.7%)

Profiling