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)

sample614.0ms (44.2%)

Results

512.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify79.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
366×	`fma-neg_binary64`
277×	`*-commutative_binary64`
262×	`exp-prod_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	20	13
3	27	13
4	46	13
5	78	13
6	146	13
7	274	13
8	670	13
9	1896	13
10	2692	13
11	3535	13
12	4713	13
13	4865	13
14	4794	13

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)

localize6.0ms (0.4%)

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 (1.2%)

Counts

2 → 16

Calls

2 calls:

14.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite11.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify77.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
684×	`fma-def_binary64`
548×	`associate-l_binary64`
292×	`times-frac_binary64`
257×	`distribute-rgt-in_binary64`

Counts

73 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1210
1	248	1114
2	549	1101
3	1241	1099
4	4205	1099
5	4980	1099

prune53.0ms (3.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Error

Counts

106 → 3

Alt Table

Status	Error	Program
	31.4b	(fma.f64 x (*.f64 x -1/2) 1)
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

Compiler

Compiled 1617 to 677 computations (58.1% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 2) (cosh.f64 x))
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

series63.0ms (4.5%)

Counts

2 → 24

Calls

2 calls:

37.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
26.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))

rewrite28.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
66×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`

Counts

2 → 118

Calls

2 calls:

15.0ms	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))
3.0ms	(/.f64 (sqrt.f64 2) (cosh.f64 x))

simplify126.0ms (9%)

Algorithm

1×	egg-herbie

Rules

640×	`associate-/l*_binary64`
573×	`fma-def_binary64`
363×	`*-commutative_binary64`
356×	`associate-/l/_binary64`
267×	`fma-neg_binary64`

Counts

142 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	2599
1	478	2383
2	1423	2028
3	3862	1982
4	4922	1982

prune199.0ms (14.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	177	3	180

Error

Counts

180 → 3

Alt Table

Status	Error	Program
▶	31.4b	(fma.f64 x (*.f64 x -1/2) 1)
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

Compiler

Compiled 3174 to 2509 computations (21% saved)

localize3.0ms (0.2%)

prune2.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	2	2
Total	3	3

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	31.4b	(fma.f64 x (*.f64 x -1/2) 1)
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.5b	(*.f64 (/.f64 (sqrt.f64 2) 2) (/.f64 (sqrt.f64 2) (cosh.f64 x)))

Compiler

Compiled 27 to 22 computations (18.5% saved)

regimes49.0ms (3.5%)

Accuracy

Total 0.1b remaining (97%)

Threshold costs 0.1b (97%)

Counts

20 → 1

Compiler

Compiled 512 to 427 computations (16.6% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	9	11

end54.0ms (3.9%)

Compiler: Compiled 43 to 36 computations (16.3% saved)

Details

analyze1.0ms (0.1%)

sample614.0ms (44.2%)

simplify79.0ms (5.6%)

prune2.0ms (0.1%)

localize6.0ms (0.4%)

series16.0ms (1.2%)

rewrite11.0ms (0.8%)

simplify77.0ms (5.5%)

prune53.0ms (3.8%)

localize6.0ms (0.4%)

series63.0ms (4.5%)

rewrite28.0ms (2%)

simplify126.0ms (9%)

prune199.0ms (14.3%)

localize3.0ms (0.2%)

prune2.0ms (0.2%)

regimes49.0ms (3.5%)

simplify2.0ms (0.2%)

end54.0ms (3.9%)

Profiling