Details

analyze4.0ms (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 (78.3%)

Results

3.3s	4304×	body	2048	valid
957.0ms	2053×	body	1024	valid
272.0ms	1002×	body	512	valid
90.0ms	513×	body	256	valid
37.0ms	384×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify26.0ms (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%)

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

31.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.2b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
▶	31.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	3.3b	(+.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)

rewrite44.0ms (0.7%)

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:

43.0ms	(-.f64 (exp.f64 x) 2)
43.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

simplify26.0ms (0.4%)

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

prune64.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

0.0b

Counts

98 → 4

Alt Table

Status	Error	Program
	31.2b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
	31.1b	(/.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)))
	31.1b	(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
▶	0.8b	(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)))))

Compiler

Compiled 1554 to 864 computations (44.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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)))))
✓	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))))

series16.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
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))))
3.0ms	(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)))))
3.0ms	(*.f64 1/20160 (pow.f64 x 8))

rewrite56.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`prod-diff_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
201×	`log-pow_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	67
1	319	67
2	3285	67

Stop Event

1×	node limit

Counts

4 → 93

Calls

4 calls:

53.0ms	(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)))))
53.0ms	(*.f64 1/20160 (pow.f64 x 8))
53.0ms	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))
53.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))

simplify55.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

505×	`distribute-rgt-out_binary64`
413×	`unswap-sqr_binary64`
379×	`distribute-lft-out_binary64`
339×	`associate-l_binary64`
316×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	528
1	63	528
2	137	528
3	392	528
4	1768	528
5	4131	528
6	4472	528
7	4968	528

Stop Event

1×	node limit

Counts

129 → 109

prune116.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Error

0.0b

Counts

113 → 4

Alt Table

Status	Error	Program
	31.2b	(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
▶	31.1b	(/.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)))
	31.1b	(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
✓	0.8b	(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)))))

Compiler

Compiled 2571 to 1945 computations (24.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) 2)
✓	0.0b	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
✓	0.0b	(/.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)))
✓	3.0b	(+.f64 (+.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) -4)))

series30.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

21.0ms	(/.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)))
5.0ms	(+.f64 (+.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) -4)))
3.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
1.0ms	(+.f64 (exp.f64 x) 2)

rewrite70.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`log1p-udef_binary64`
153×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`
147×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	74
1	309	70
2	4691	70

Stop Event

1×	node limit

Counts

4 → 142

Calls

4 calls:

67.0ms	(+.f64 (exp.f64 x) 2)
67.0ms	(*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))
67.0ms	(/.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)))
67.0ms	(+.f64 (+.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) (+.f64 (exp.f64 (+.f64 x x)) -4)))

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-r_binary64`
701×	`unswap-sqr_binary64`
327×	`fma-def_binary64`
269×	`times-frac_binary64`
188×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	767
1	176	715
2	468	646
3	1450	646
4	3477	646

Stop Event

1×	node limit

Counts

190 → 177

prune155.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	216	3	219

Error

Counts

219 → 3

Alt Table

Status	Error	Program
	31.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) 2) 3) (pow.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -4)) 3)) (+.f64 (pow.f64 (+.f64 (exp.f64 x) 2) 2) (.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -4)) (-.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -4)) (+.f64 (exp.f64 x) 2))))) (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
▶	31.1b	(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
✓	0.8b	(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)))))

Compiler

Compiled 6333 to 3840 computations (39.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 x) 2)
✓	0.0b	(/.f64 1 (+.f64 (exp.f64 x) 2))
✓	0.0b	(*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2)))
✓	2.8b	(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))

series34.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

18.0ms

(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))

8.0ms

(*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2)))

7.0ms

(/.f64 1 (+.f64 (exp.f64 x) 2))

rewrite135.0ms (2.2%)

Algorithm

4×	egg-rewrite
1×	batch-egg-rewrite

Rules

755×	`log1p-expm1-u_binary64`
755×	`expm1-log1p-u_binary64`
471×	`prod-diff_binary64`
321×	`expm1-udef_binary64`
321×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	332	58
0	15	24
1	332	24
0	15	27
0	12	17
1	263	6
2	3448	6
0	7	9
1	146	9
2	1728	9

Stop Event

1×	node limit
1×	node limit
1×	iter limit
1×	node limit
1×	node limit

Counts

3 → 79

Calls

3 calls:

134.0ms

(/.f64 1 (+.f64 (exp.f64 x) 2))

134.0ms

(*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2)))

134.0ms

(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))

simplify39.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
722×	`fma-def_binary64`
620×	`associate-l_binary64`
451×	`associate-r_binary64`
133×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	539
1	169	535
2	391	531
3	1166	520
4	4408	519

Stop Event

1×	node limit

Counts

115 → 107

prune135.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
	31.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (exp.f64 x) 2) 3) (pow.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -4)) 3)) (+.f64 (pow.f64 (+.f64 (exp.f64 x) 2) 2) (.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -4)) (-.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (.f64 (exp.f64 x) -4)) (+.f64 (exp.f64 x) 2))))) (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2)))
✓	31.1b	(+.f64 (*.f64 (+.f64 (exp.f64 (+.f64 x x)) -4) (/.f64 1 (+.f64 (exp.f64 x) 2))) (exp.f64 (neg.f64 x)))
✓	0.8b	(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)))))

Compiler

Compiled 2989 to 1762 computations (41.1% saved)

regimes111.0ms (1.8%)

Accuracy

Total 0.6b remaining (92.7%)

Threshold costs 0.6b (92.7%)

Counts

68 → 1

Compiler

Compiled 2166 to 1566 computations (27.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25

Stop Event

1×

saturated

end100.0ms (1.7%)

Compiler: Compiled 134 to 94 computations (29.9% saved)

Details

analyze4.0ms (0.1%)

sample4.7s (78.3%)

simplify26.0ms (0.4%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite44.0ms (0.7%)

simplify26.0ms (0.4%)

prune64.0ms (1.1%)

localize10.0ms (0.2%)

series16.0ms (0.3%)

rewrite56.0ms (0.9%)

simplify55.0ms (0.9%)

prune116.0ms (1.9%)

localize10.0ms (0.2%)

series30.0ms (0.5%)

rewrite70.0ms (1.2%)

simplify41.0ms (0.7%)

prune155.0ms (2.6%)

localize10.0ms (0.2%)

series34.0ms (0.6%)

rewrite135.0ms (2.2%)

simplify39.0ms (0.7%)

prune135.0ms (2.2%)

regimes111.0ms (1.8%)

simplify2.0ms (0%)

end100.0ms (1.7%)

Profiling