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)

sample4.8s (80.5%)

Results

3.4s	4364×	body	2048	valid
889.0ms	2025×	body	1024	valid
276.0ms	1017×	body	512	valid
95.0ms	502×	body	256	valid
43.0ms	348×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

prune2.0ms (0%)

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

29.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	2.6b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series4.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`

Counts

2 → 69

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
326×	`fma-def_binary64`
296×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
268×	`distribute-rgt-out_binary64`

Counts

85 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1174
1	295	959
2	717	942
3	2801	932
4	4435	932
5	4838	932

prune75.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	3	115

Error

0.0b

Counts

115 → 3

Alt Table

Status	Error	Program
▶	0.8b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
	29.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	1.3b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 2096 to 1199 computations (42.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
✓	0.0b	(*.f64 1/360 (pow.f64 x 6))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series15.0ms (0.2%)

Counts

4 → 9

Calls

4 calls:

5.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
3.0ms	(*.f64 1/360 (pow.f64 x 6))
3.0ms	(*.f64 1/20160 (pow.f64 x 8))
3.0ms	(*.f64 1/12 (pow.f64 x 4))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
19×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

4 → 98

Calls

4 calls:

11.0ms	(+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
5.0ms	(*.f64 1/12 (pow.f64 x 4))
4.0ms	(*.f64 1/20160 (pow.f64 x 8))
4.0ms	(*.f64 1/360 (pow.f64 x 6))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

502×	`distribute-rgt-in_binary64`
476×	`distribute-lft-in_binary64`
410×	`unswap-sqr_binary64`
373×	`*-commutative_binary64`
369×	`fma-def_binary64`

Counts

107 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	1560
1	384	1472
2	1127	1398
3	3623	1396
4	4926	1396

prune163.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	140	3	143

Error

0.0b

Counts

143 → 3

Alt Table

Status	Error	Program
▶	0.8b	(expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))
	29.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	3.7b	(exp.f64 (log.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))))

Compiler

Compiled 3906 to 3150 computations (19.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))))
✓	0.0b	(expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))
	0.0b	(*.f64 1/20160 (pow.f64 x 8))
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))

series18.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

8.0ms

(log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))))

5.0ms

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

4.0ms

(expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms

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

0.0ms

(log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8))))))

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

422×	`associate-+l+_binary64`
339×	`associate-+r+_binary64`
320×	`cancel-sign-sub-inv_binary64`
228×	`fma-def_binary64`
224×	`exp-prod_binary64`

Counts

68 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1541
1	221	1394
2	538	1378
3	1845	1378
4	4724	1378
5	4977	1378
6	4958	1378

prune126.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	116	4	120

Error

0.0b

Counts

120 → 4

Alt Table

Status	Error	Program
✓	0.8b	(expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))
	29.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	3.7b	(exp.f64 (log.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))))
▶	1.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))

Compiler

Compiled 2987 to 2311 computations (22.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series21.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))
4.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
0.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

622×	`associate-l_binary64`
594×	`exp-prod_binary64`
535×	`associate-r_binary64`
476×	`unswap-sqr_binary64`
382×	`distribute-lft-in_binary64`

Counts

44 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	689
1	61	629
2	131	629
3	468	629
4	2907	629
5	4705	629
6	5220	629

prune70.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	72	4	76

Error

0.0b

Counts

76 → 4

Alt Table

Status	Error	Program
✓	0.8b	(expm1.f64 (log1p.f64 (fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/20160 (pow.f64 x 8)))))))
	29.2b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
	3.7b	(exp.f64 (log.f64 (+.f64 (.f64 1/12 (pow.f64 x 4)) (+.f64 (.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))))
✓	1.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))

Compiler

Compiled 1397 to 1018 computations (27.1% saved)

regimes76.0ms (1.3%)

Accuracy

Total 0.5b remaining (98.6%)

Threshold costs 0.5b (98.6%)

Counts

42 → 1

Compiler

Compiled 1350 to 984 computations (27.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	18	29
2	18	29

end102.0ms (1.7%)

Compiler: Compiled 110 to 85 computations (22.7% saved)

Details

analyze5.0ms (0.1%)

sample4.8s (80.5%)

simplify57.0ms (1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite16.0ms (0.3%)

simplify90.0ms (1.5%)

prune75.0ms (1.3%)

localize12.0ms (0.2%)

series15.0ms (0.2%)

rewrite28.0ms (0.5%)

simplify71.0ms (1.2%)

prune163.0ms (2.8%)

localize15.0ms (0.3%)

series18.0ms (0.3%)

rewrite2.0ms (0%)

simplify95.0ms (1.6%)

prune126.0ms (2.1%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite1.0ms (0%)

simplify76.0ms (1.3%)

prune70.0ms (1.2%)

regimes76.0ms (1.3%)

simplify2.0ms (0%)

end102.0ms (1.7%)

Profiling