Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample4.7s (83.3%)

Results

3.4s	4339×	body	2048	valid
885.0ms	2069×	body	1024	valid
282.0ms	958×	body	512	valid
86.0ms	492×	body	256	valid
39.0ms	398×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`
284×	`cancel-sign-sub-inv_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	36	13
3	60	13
4	122	13
5	272	13
6	697	13
7	1699	13
8	3110	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

26.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	26.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
	26.9b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	3.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

2.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
1.0ms	(-.f64 (exp.f64 x) 2)

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

815×	`expm1-log1p-u_binary64`
536×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`log1p-expm1-u_binary64`
88×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	181	17
2	2616	17

Stop Event

1×	node limit

Counts

2 → 78

Calls

2 calls:

48.0ms	(-.f64 (exp.f64 x) 2)
48.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

749×	`unswap-sqr_binary64`
544×	`associate-l_binary64`
523×	`fma-def_binary64`
398×	`associate-r_binary64`
193×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	198
1	115	196
2	250	196
3	744	191
4	3163	191

Stop Event

1×	node limit

Counts

94 → 96

prune108.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Error

0.0b

Counts

98 → 4

Alt Table

Status	Error	Program
✓	26.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	1.1b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
	26.9b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
	26.9b	(/.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) -4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))

Compiler

Compiled 1527 to 843 computations (44.8% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.1b	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
✓	0.1b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))

series11.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))
4.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
3.0ms	(*.f64 1/20160 (pow.f64 x 8))

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
184×	`log-pow_binary64`
152×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	299	42
2	3039	42

Stop Event

1×	node limit

Counts

3 → 75

Calls

3 calls:

48.0ms	(*.f64 1/20160 (pow.f64 x 8))
48.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
48.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
472×	`unswap-sqr_binary64`
392×	`*-commutative_binary64`
369×	`sqr-pow_binary64`
244×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	336
1	37	336
2	81	336
3	219	336
4	733	336
5	1611	336
6	3015	336
7	3342	336
8	3527	336
9	3732	336
10	4007	336
11	4363	336
12	4772	336

Stop Event

1×	node limit

Counts

99 → 83

prune94.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	83	4	87

Error

0.0b

Counts

87 → 4

Alt Table

Status	Error	Program
✓	26.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.1b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
▶	26.9b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
	26.9b	(/.f64 (+.f64 (+.f64 (exp.f64 x) 2) (.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) -4))) (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))

Compiler

Compiled 2081 to 1590 computations (23.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (neg.f64 x)) -2)
✓	3.0b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
1.0ms	(+.f64 (exp.f64 (neg.f64 x)) -2)

rewrite41.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`expm1-log1p-u_binary64`
636×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
88×	`log1p-expm1-u_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	179	15
2	2582	15

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

40.0ms	(+.f64 (exp.f64 (neg.f64 x)) -2)
40.0ms	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

749×	`unswap-sqr_binary64`
623×	`fma-neg_binary64`
554×	`associate-l_binary64`
507×	`fma-def_binary64`
411×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	268
1	120	260
2	265	260
3	832	260
4	3789	259

Stop Event

1×	node limit

Counts

93 → 90

prune61.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	90	4	94

Error

0.0b

Counts

94 → 4

Alt Table

Status	Error	Program
✓	26.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.1b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
▶	27.7b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	26.9b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 1275 to 811 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
✓	2.0b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	2.1b	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

series31.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
10.0ms	(+.f64 -2 (*.f64 2 (cosh.f64 x)))
10.0ms	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))

rewrite49.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
140×	`prod-diff_binary64`
92×	`egg-rr`
83×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	176	23
2	2056	23

Stop Event

1×	node limit

Counts

3 → 92

Calls

3 calls:

48.0ms	(exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))
48.0ms	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
48.0ms	(+.f64 -2 (*.f64 2 (cosh.f64 x)))

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

530×	`distribute-rgt-out_binary64`
482×	`distribute-lft-out_binary64`
439×	`fma-def_binary64`
437×	`*-commutative_binary64`
413×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	487
1	97	483
2	226	481
3	598	481
4	2433	481

Stop Event

1×	node limit

Counts

128 → 79

prune58.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	79	4	83

Error

0.0b

Counts

83 → 4

Alt Table

Status	Error	Program
✓	26.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	1.1b	(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))
✓	27.7b	(log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))
✓	26.9b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

Compiler

Compiled 1046 to 804 computations (23.1% saved)

regimes61.0ms (1.1%)

Accuracy

Total 0.0b remaining (20%)

Threshold costs 0.0b (20%)

Counts

37 → 2

Compiler

Compiled 808 to 598 computations (26% saved)

bsearch1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	56
1	34	56
2	37	56
3	38	56

Stop Event

1×

saturated

end90.0ms (1.6%)

Compiler: Compiled 122 to 88 computations (27.9% saved)

Details

analyze5.0ms (0.1%)

sample4.7s (83.3%)

simplify25.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite50.0ms (0.9%)

simplify30.0ms (0.5%)

prune108.0ms (1.9%)

localize13.0ms (0.2%)

series11.0ms (0.2%)

rewrite50.0ms (0.9%)

simplify71.0ms (1.3%)

prune94.0ms (1.6%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite41.0ms (0.7%)

simplify33.0ms (0.6%)

prune61.0ms (1.1%)

localize6.0ms (0.1%)

series31.0ms (0.5%)

rewrite49.0ms (0.9%)

simplify39.0ms (0.7%)

prune58.0ms (1%)

regimes61.0ms (1.1%)

bsearch1.0ms (0%)

simplify3.0ms (0%)

end90.0ms (1.6%)

Profiling