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)

sample1.7s (71.5%)

Results

1.7s

8256×

body

256

valid

Compiler

Compiled 54 to 44 computations (18.5% saved)

preprocess35.0ms (1.4%)

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

rewrite32.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

445×	`pow1_binary64`
414×	`add-log-exp_binary64`
414×	`log1p-expm1-u_binary64`
414×	`expm1-log1p-u_binary64`
406×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	102	11
2	1142	11

Stop Event

1×	node limit

Counts

2 → 24

simplify64.0ms (2.7%)

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

48 → 27

prune19.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	21	6	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	7	28

Error

0.0b

Counts

28 → 7

Alt Table

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

Compiler

Compiled 309 to 235 computations (23.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 1/25000000000000000000000000000000 (pow.f64 t 2))

series3.0ms (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

rewrite34.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`pow1_binary64`
445×	`add-log-exp_binary64`
445×	`log1p-expm1-u_binary64`
445×	`expm1-log1p-u_binary64`
436×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1268	7

Stop Event

1×	node limit

Counts

1 → 11

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

11 → 11

prune27.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	13	5	18

Error

0.0b

Counts

18 → 5

Alt Table

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

Compiler

Compiled 149 to 108 computations (27.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series8.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

3.0ms	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))	t	0
1.0ms	(*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000)	t	0
1.0ms	(*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000)	t	inf
1.0ms	(*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000)	t	-inf
1.0ms	(sqrt.f64 (*.f64 (pow.f64 t 4) 1/625000000000000000000000000000000000000000000000000000000000000))	t	inf

rewrite37.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

573×	`pow1_binary64`
539×	`add-log-exp_binary64`
539×	`log1p-expm1-u_binary64`
539×	`expm1-log1p-u_binary64`
526×	`add-exp-log_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 → 36

simplify72.0ms (3%)

Algorithm

1×	egg-herbie

Rules

616×	`sqr-pow_binary64`
396×	`associate-l_binary64`
342×	`unswap-sqr_binary64`
327×	`pow-sqr_binary64`
298×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	168
1	19	168
2	39	168
3	90	168
4	285	168
5	1158	168
6	1908	168
7	2032	168
8	2201	168
9	2400	168
10	2673	168
11	3032	168
12	3483	168
13	4005	168
14	4635	168

Stop Event

1×	node limit

Counts

60 → 39

prune30.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	2	1	3
Picked	1	0	1
Done	1	0	1
Total	40	4	44

Error

Counts

44 → 4

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
▶	0.2b	(sqrt.f64 (sqrt.f64 (*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))))
	0.5b	(.f64 1/25000000000000000000000000000000 (.f64 t t))
	0.5b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))

Compiler

Compiled 373 to 281 computations (24.7% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (sqrt.f64 (*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))))
✓	0.1b	(sqrt.f64 (*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8)))
✓	0.4b	(*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))

series9.0ms (0.4%)

Counts

3 → 24

Calls

9 calls:

1.0ms	(*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))	t	inf
1.0ms	(*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))	t	0
1.0ms	(*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))	t	-inf
1.0ms	(sqrt.f64 (*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8)))	t	-inf
1.0ms	(sqrt.f64 (*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8)))	t	inf

rewrite46.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

650×	`pow1_binary64`
610×	`add-log-exp_binary64`
610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
73×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	168	23
2	1783	23

Stop Event

1×	node limit

Counts

3 → 66

simplify71.0ms (3%)

Algorithm

1×	egg-herbie

Rules

616×	`sqr-pow_binary64`
396×	`associate-l_binary64`
342×	`unswap-sqr_binary64`
327×	`pow-sqr_binary64`
298×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	168
1	19	168
2	39	168
3	90	168
4	285	168
5	1158	168
6	1908	168
7	2032	168
8	2201	168
9	2400	168
10	2673	168
11	3032	168
12	3483	168
13	4005	168
14	4635	168

Stop Event

1×	node limit

Counts

90 → 68

prune37.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	68	4	72

Error

Counts

72 → 4

Alt Table

Status	Error	Program
	0.4b	(*.f64 1/25000000000000000000000000000000 (sqrt.f64 (pow.f64 t 4)))
✓	0.2b	(sqrt.f64 (sqrt.f64 (*.f64 1/390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (pow.f64 t 8))))
	0.5b	(pow.f64 (*.f64 t 1/5000000000000000) 2)
	0.5b	(.f64 (.f64 t t) (pow.f64 1/625000000000000000000000000000000000000000000000000000000000000 1/2))

Compiler

Compiled 728 to 636 computations (12.6% saved)

regimes55.0ms (2.3%)

Accuracy

Total 0.2b remaining (96.3%)

Threshold costs 0.2b (96.3%)

Counts

20 → 1

Compiler

Compiled 590 to 472 computations (20% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

end56.0ms (2.3%)

Stop Event

1×

fuel

Compiler

Compiled 45 to 38 computations (15.6% saved)

Details

analyze1.0ms (0%)

sample1.7s (71.5%)

preprocess35.0ms (1.4%)

simplify22.0ms (0.9%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite32.0ms (1.3%)

simplify64.0ms (2.7%)

prune19.0ms (0.8%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite34.0ms (1.4%)

simplify6.0ms (0.3%)

prune27.0ms (1.1%)

localize4.0ms (0.2%)

series8.0ms (0.3%)

rewrite37.0ms (1.6%)

simplify72.0ms (3%)

prune30.0ms (1.3%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite46.0ms (1.9%)

simplify71.0ms (3%)

prune37.0ms (1.5%)

regimes55.0ms (2.3%)

simplify2.0ms (0.1%)

end56.0ms (2.3%)

Profiling