Details

analyze0.0ms (0%)

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)

sample735.0ms (47.4%)

Results

722.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess37.0ms (2.4%)

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)

simplify28.0ms (1.8%)

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

prune1.0ms (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))))

series16.0ms (1%)

Counts

2 → 16

Calls

6 calls:

8.0ms	(/.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
0.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))	x	inf

rewrite74.0ms (4.8%)

Algorithm

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

Rules

88×	`add-sqr-sqrt_binary64`
88×	`add-sqr-sqrt_binary64`
85×	`log1p-expm1-u_binary64`
85×	`expm1-log1p-u_binary64`
85×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	18
2	2796	18
0	8	9
1	176	9
2	2796	9
0	8	9
0	6	6
1	129	6
2	2130	6
0	6	6

Stop Event

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

Counts

2 → 22

simplify28.0ms (1.8%)

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

prune30.0ms (1.9%)

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 (0.4%)

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))))

series265.0ms (17.1%)

Counts

2 → 24

Calls

6 calls:

124.0ms	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))	x	inf
118.0ms	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))	x	-inf
11.0ms	(/.f64 2 (*.f64 2 (cosh.f64 x)))	x	-inf
10.0ms	(/.f64 2 (*.f64 2 (cosh.f64 x)))	x	inf
1.0ms	(log.f64 (/.f64 2 (*.f64 2 (cosh.f64 x))))	x	0

rewrite40.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

627×	`log1p-expm1-u_binary64`
627×	`expm1-log1p-u_binary64`
331×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	150	13
2	1752	13

Stop Event

1×	node limit

Counts

2 → 78

simplify36.0ms (2.3%)

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

102 → 97

prune66.0ms (4.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	97	2	99

Error

Counts

99 → 2

Alt Table

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

Compiler

Compiled 1359 to 926 computations (31.9% 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)))

series2.0ms (0.1%)

Counts

1 → 4

Calls

3 calls:

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

rewrite32.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
326×	`unpow-prod-down_binary64`
263×	`log-prod_binary64`
156×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	140	9
2	1476	9

Stop Event

1×	node limit

Counts

1 → 39

simplify20.0ms (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

43 → 46

prune27.0ms (1.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	46	2	48

Error

Counts

48 → 2

Alt Table

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

Compiler

Compiled 589 to 362 computations (38.5% saved)

regimes55.0ms (3.6%)

Accuracy

Total 0.0b remaining (12.4%)

Threshold costs 0.0b (12.4%)

Counts

23 → 1

Compiler

Compiled 685 to 570 computations (16.8% 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

end41.0ms (2.7%)

Stop Event

1×

done

Compiler

Compiled 32 to 28 computations (12.5% saved)

Details

analyze0.0ms (0%)

sample735.0ms (47.4%)

preprocess37.0ms (2.4%)

simplify28.0ms (1.8%)

prune1.0ms (0.1%)

localize5.0ms (0.3%)

series16.0ms (1%)

rewrite74.0ms (4.8%)

simplify28.0ms (1.8%)

prune30.0ms (1.9%)

localize5.0ms (0.4%)

series265.0ms (17.1%)

rewrite40.0ms (2.6%)

simplify36.0ms (2.3%)

prune66.0ms (4.3%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite32.0ms (2%)

simplify20.0ms (1.3%)

prune27.0ms (1.7%)

regimes55.0ms (3.6%)

simplify2.0ms (0.1%)

end41.0ms (2.7%)

Profiling