Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample772.0ms (50.1%)

Results

760.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess41.0ms (2.7%)

Algorithm

2×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
366×	`fma-def_binary64`
257×	`associate-/l*_binary64`
247×	`*-commutative_binary64`
242×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	419	13
8	1133	13
9	3111	13
10	4302	13
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify30.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
366×	`fma-def_binary64`
257×	`associate-/l*_binary64`
247×	`*-commutative_binary64`
242×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	419	13
8	1133	13
9	3111	13
10	4302	13

Stop Event

1×	node limit

Counts

1 → 1

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series15.0ms (0.9%)

Counts

2 → 16

Calls

6 calls:

6.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	-inf
5.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	inf
1.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))	x	0
1.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))	x	0
1.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))	x	inf

rewrite79.0ms (5.1%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

91×	`add-sqr-sqrt_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`add-log-exp_binary64`
87×	`add-log-exp_binary64`
85×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	18
2	2824	18
0	8	9
1	176	9
2	2824	9
0	8	9
0	6	6
1	129	6
2	2129	6
0	6	6

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 22

simplify27.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-neg_binary64`
391×	`distribute-rgt-neg-in_binary64`
370×	`fma-def_binary64`
346×	`distribute-lft-neg-in_binary64`
330×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	187
1	89	183
2	217	177
3	655	175
4	2761	175

Stop Event

1×	node limit

Counts

38 → 40

prune26.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	2	41

Error

Counts

41 → 2

Alt Table

Status	Error	Program
▶	0.0b	(exp.f64 (log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
	31.7b	(fma.f64 x (*.f64 x -1/2) 1)

Compiler

Compiled 488 to 342 computations (29.9% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))
✓	3.1b	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))

series249.0ms (16.1%)

Counts

2 → 24

Calls

6 calls:

118.0ms	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))	x	inf
109.0ms	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))	x	-inf
9.0ms	(/.f64 2 (*.f64 2 (cosh.f64 x)))	x	-inf
9.0ms	(/.f64 2 (*.f64 2 (cosh.f64 x)))	x	inf
3.0ms	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))	x	0

rewrite41.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`pow1_binary64`
628×	`add-log-exp_binary64`
627×	`log1p-expm1-u_binary64`
627×	`expm1-log1p-u_binary64`
74×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	150	13
2	1773	13

Stop Event

1×	node limit

Counts

2 → 49

simplify34.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

538×	`associate-l_binary64`
502×	`fma-def_binary64`
413×	`unswap-sqr_binary64`
410×	`associate-r_binary64`
329×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	352
1	101	350
2	258	342
3	888	340
4	4273	340

Stop Event

1×	node limit

Counts

73 → 68

prune41.0ms (2.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	68	2	70

Error

Counts

70 → 2

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
▶	0.2b	(exp.f64 (*.f64 -1/2 (pow.f64 x 2)))

Compiler

Compiled 777 to 515 computations (33.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (*.f64 -1/2 (pow.f64 x 2)))

series4.0ms (0.2%)

Counts

1 → 4

Calls

3 calls:

2.0ms	(exp.f64 (*.f64 -1/2 (pow.f64 x 2)))	x	-inf
1.0ms	(exp.f64 (*.f64 -1/2 (pow.f64 x 2)))	x	0
1.0ms	(exp.f64 (*.f64 -1/2 (pow.f64 x 2)))	x	inf

rewrite32.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`pow1_binary64`
511×	`add-log-exp_binary64`
511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
500×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	141	9
2	1460	9

Stop Event

1×	node limit

Counts

1 → 23

simplify19.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

983×	`fma-neg_binary64`
395×	`distribute-rgt-neg-in_binary64`
348×	`distribute-lft-neg-in_binary64`
285×	`unswap-sqr_binary64`
229×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	54	52
2	136	48
3	446	46
4	1960	46

Stop Event

1×	node limit

Counts

27 → 30

prune16.0ms (1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	30	2	32

Error

Counts

32 → 2

Alt Table

Status	Error	Program
✓	0.0b	(exp.f64 (log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
✓	0.2b	(exp.f64 (*.f64 -1/2 (pow.f64 x 2)))

Compiler

Compiled 313 to 204 computations (34.8% saved)

regimes52.0ms (3.4%)

Accuracy

Total 0.0b remaining (12.4%)

Threshold costs 0.0b (12.4%)

Counts

21 → 1

Compiler

Compiled 640 to 531 computations (17% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	12	13
2	14	13
3	15	13

Stop Event

1×

saturated

end46.0ms (3%)

Stop Event

1×

done

Compiler

Compiled 32 to 28 computations (12.5% saved)

Details

analyze1.0ms (0.1%)

sample772.0ms (50.1%)

preprocess41.0ms (2.7%)

simplify30.0ms (1.9%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series15.0ms (0.9%)

rewrite79.0ms (5.1%)

simplify27.0ms (1.7%)

prune26.0ms (1.7%)

localize5.0ms (0.3%)

series249.0ms (16.1%)

rewrite41.0ms (2.7%)

simplify34.0ms (2.2%)

prune41.0ms (2.7%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite32.0ms (2.1%)

simplify19.0ms (1.3%)

prune16.0ms (1%)

regimes52.0ms (3.4%)

simplify2.0ms (0.1%)

end46.0ms (3%)

Profiling