Details

analyze74.0ms (1.2%)

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)

sample104.0ms (1.7%)

Algorithm

1×

intervals

Results

74.0ms	131×	body	2048	valid
19.0ms	75×	body	1024	valid
3.0ms	21×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	15×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify62.0ms (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 → 0

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

1 alts after pruning (1 fresh and 0 done)

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

Error

29.4b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	29.4b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
4.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite87.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

29.3b

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:

7.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 1319 to 782 computations (40.7% saved)

series20.0ms (0.3%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

6.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
6.0ms	(-.f64 (exp.f64 x) 2)

Compiler

Compiled 292 to 218 computations (25.3% saved)

simplify85.0ms (1.4%)

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

81 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	968
1	295	893
2	717	876
3	2801	866
4	4435	866
5	4838	866

prune34.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	4	60

Error

0.0b

Counts

60 → 4

Alt Table

Status	Error	Program
	29.4b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
	29.5b	(log.f64 (exp.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)))
▶	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	0.7b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 725 to 386 computations (46.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
0.0b	(*.f64 1/20160 (pow.f64 x 8))

rewrite65.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 57

Calls

4 calls:

4.0ms	(*.f64 1/20160 (pow.f64 x 8))
0.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
0.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
0.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

Compiler

Compiled 1414 to 1057 computations (25.2% saved)

series73.0ms (1.2%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

22.0ms	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
18.0ms	(fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))
14.0ms	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
7.0ms	(*.f64 1/20160 (pow.f64 x 8))

Compiler

Compiled 869 to 692 computations (20.4% saved)

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
610×	`associate-+r+_binary64`
610×	`associate-+l+_binary64`
262×	`associate-l_binary64`
230×	`associate-r_binary64`

Counts

87 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1406
1	172	1283
2	418	1265
3	1707	1265
4	5576	1265

prune44.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
	29.4b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
	29.5b	(log.f64 (exp.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)))
✓	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
▶	0.7b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 996 to 720 computations (27.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/12 (pow.f64 x 4))
0.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 501 to 359 computations (28.3% saved)

series19.0ms (0.3%)

Error

0.0b

Counts

2 → 9

Calls

2 calls:

13.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
5.0ms	(*.f64 1/12 (pow.f64 x 4))

Compiler

Compiled 156 to 116 computations (25.6% saved)

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
562×	`unswap-sqr_binary64`
352×	`*-commutative_binary64`
333×	`distribute-rgt-out_binary64`
291×	`distribute-lft-out_binary64`

Counts

46 → 27

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	66	525
1	110	490
2	240	472
3	668	472
4	1295	466
5	3475	461
6	4962	461
7	4950	461

prune19.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	27	4	31

Error

0.0b

Counts

31 → 4

Alt Table

Status	Error	Program
▶	29.4b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
	29.5b	(log.f64 (exp.f64 (-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)))
✓	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.7b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

Compiler

Compiled 343 to 217 computations (36.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
0.0b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
0.1b	(pow.f64 (exp.f64 x) 3)
3.5b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))

rewrite112.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 93

Calls

4 calls:

6.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
4.0ms	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
3.0ms	(pow.f64 (exp.f64 x) 3)
3.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))

Compiler

Compiled 3403 to 2022 computations (40.6% saved)

series76.0ms (1.3%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

29.0ms	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
13.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8)))))
10.0ms	(*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))
9.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 1391 to 940 computations (32.4% saved)

simplify176.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-neg_binary64`
321×	`exp-prod_binary64`
317×	`unswap-sqr_binary64`
224×	`associate-l_binary64`
211×	`cancel-sign-sub-inv_binary64`

Counts

117 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	3157
1	495	2540
2	2254	2495
3	4026	2495
4	4925	2495
5	4942	2495

prune139.0ms (2.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	81	5	86

Error

0.0b

Counts

86 → 5

Alt Table

Status	Error	Program
	0.5b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	29.2b	(/.f64 1 (/.f64 (exp.f64 x) (/.f64 (fma.f64 (exp.f64 x) (+.f64 (+.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 3)) -6) 4) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4))))
	29.4b	(/.f64 (+.f64 4 (.f64 (exp.f64 x) (+.f64 2 (+.f64 (exp.f64 x) (-.f64 (pow.f64 (exp.f64 x) 3) 8))))) (.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))
	0.7b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	29.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (exp.f64 x) (+.f64 (+.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 3)) -6) 4)) (cbrt.f64 (fma.f64 (exp.f64 x) (+.f64 (+.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 3)) -6) 4))) (cbrt.f64 (fma.f64 (exp.f64 x) (+.f64 (+.f64 (exp.f64 x) (pow.f64 (exp.f64 x) 3)) -6) 4))) (*.f64 (exp.f64 x) (fma.f64 (exp.f64 x) (+.f64 2 (exp.f64 x)) 4)))

Compiler

Compiled 2079 to 1211 computations (41.8% saved)

regimes272.0ms (4.5%)

Accuracy

Total 0.5b remaining (82.9%)

Threshold costs 0.5b (82.9%)

Compiler

Compiled 2944 to 2014 computations (31.6% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	16	25
2	16	25

end1.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample4.4s (71.7%)

Algorithm

1×

intervals

Results

2.9s	4161×	body	2048	valid
669.0ms	1994×	body	1024	valid
175.0ms	966×	body	512	valid
54.0ms	503×	body	256	valid
20.0ms	376×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 172 to 112 computations (34.9% saved)

Details

analyze74.0ms (1.2%)

sample104.0ms (1.7%)

simplify62.0ms (1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite87.0ms (1.4%)

series20.0ms (0.3%)

simplify85.0ms (1.4%)

prune34.0ms (0.6%)

localize10.0ms (0.2%)

rewrite65.0ms (1.1%)

series73.0ms (1.2%)

simplify64.0ms (1.1%)

prune44.0ms (0.7%)

localize5.0ms (0.1%)

rewrite36.0ms (0.6%)

series19.0ms (0.3%)

simplify102.0ms (1.7%)

prune19.0ms (0.3%)

localize15.0ms (0.3%)

rewrite112.0ms (1.8%)

series76.0ms (1.3%)

simplify176.0ms (2.9%)

prune139.0ms (2.3%)

regimes272.0ms (4.5%)

simplify10.0ms (0.2%)

end1.0ms (0%)

sample4.4s (71.7%)

Profiling