Details

analyze8.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample53.0ms (1.3%)

Algorithm

1×

intervals

Results

8.0ms	46×	body	1024	valid
8.0ms	48×	body	512	valid
6.0ms	133×	body	128	valid
3.0ms	29×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.0b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	2.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series13.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite182.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
18.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify405.0ms (9.6%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
457×	`times-frac_binary64`
236×	`fma-def_binary64`
186×	`sub-neg_binary64`
176×	`exp-prod_binary64`

Counts

716 → 853

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	19278
1	989	13709
2	2519	9843
3	4349	9843
4	4815	9843

prune896.0ms (21.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	849	4	853
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	850	4	854

Error

0.2b

Counts

854 → 4

Alt Table

Status	Error	Program
	26.9b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
	27.7b	(+.f64 (/.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (*.f64 (+.f64 x 1) x)) (/.f64 1 (-.f64 x 1)))
▶	13.0b	(+.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x)) (/.f64 1 (-.f64 x 1)))
	30.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 33721 to 26238 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x))
	0.0b	(/.f64 1 (-.f64 x 1))
✓	2.1b	(+.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x)) (/.f64 1 (-.f64 x 1)))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(+.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64`
33×	`distribute-lft-out_binary64`
32×	`times-frac_binary64`
25×	`fma-def_binary64`
11×	`add-sqr-sqrt_binary64`

Counts

2 → 71

Calls

2 calls:

27.0ms	(+.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x)) (/.f64 1 (-.f64 x 1)))
16.0ms	(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
395×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`
265×	`associate-l_binary64`
249×	`associate-r_binary64`

Counts

95 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1663
1	389	1576
2	1202	1550
3	4866	1550
4	4934	1550

prune192.0ms (4.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	236	4	240

Error

0.2b

Counts

240 → 4

Alt Table

Status	Error	Program
▶	26.9b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
	27.7b	(+.f64 (/.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (*.f64 (+.f64 x 1) x)) (/.f64 1 (-.f64 x 1)))
✓	13.0b	(+.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x)) (/.f64 1 (-.f64 x 1)))
	30.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 5472 to 4397 computations (19.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	15.3b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

series8.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
2.0ms	(*.f64 (+.f64 x 1) x)
1.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
1.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`associate-*l/_binary64`
41×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
37×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

4 → 153

Calls

4 calls:

18.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
9.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
6.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
4.0ms	(*.f64 (+.f64 x 1) x)

simplify100.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

613×	`associate-+l+_binary64`
601×	`associate-l_binary64`
445×	`associate-r_binary64`
364×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`

Counts

201 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3792
1	791	3063
2	3278	2739
3	5428	2739

prune295.0ms (7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	294	1	295
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	295	4	299

Error

0.2b

Counts

299 → 4

Alt Table

Status	Error	Program
✓	13.0b	(+.f64 (+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 x)) (/.f64 1 (-.f64 x 1)))
	27.7b	(+.f64 (/.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (*.f64 (+.f64 x 1) x)) (/.f64 1 (-.f64 x 1)))
▶	0.3b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
	30.6b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))

Compiler

Compiled 13314 to 9744 computations (26.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x 1) x)
	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.2b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`associate-/r/_binary64`
8×	`associate-*l/_binary64`
4×	`frac-times_binary64`

Counts

1 → 33

Calls

1 calls:

9.0ms

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

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

736×	`associate-l_binary64`
481×	`distribute-rgt-in_binary64`
462×	`associate-/r*_binary64`
437×	`distribute-lft-in_binary64`
371×	`fma-neg_binary64`

Counts

45 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	126	975
1	335	727
2	1109	699
3	4461	672
4	4853	671
5	4990	671

prune188.0ms (4.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	186	6	192
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	190	6	196

Error

0.0b

Counts

196 → 6

Alt Table

Status	Error	Program
	3.7b	(.f64 (/.f64 2 (.f64 (.f64 (-.f64 (.f64 x x) (*.f64 1 1)) x) (-.f64 x 1))) (-.f64 x 1))
	0.2b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
	0.5b	(/.f64 2 (.f64 (.f64 (fma.f64 x x x) (*.f64 (cbrt.f64 (+.f64 -1 x)) (cbrt.f64 (+.f64 -1 x)))) (cbrt.f64 (-.f64 x 1))))
	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
	0.7b	(/.f64 (sqrt.f64 2) (/.f64 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)) (sqrt.f64 2)))

Compiler

Compiled 3851 to 2826 computations (26.6% saved)

regimes427.0ms (10.1%)

Accuracy

Total 0.1b remaining (89.8%)

Threshold costs 0.1b (89.8%)

Counts

199 → 1

Compiler

Compiled 8130 to 6689 computations (17.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	13	14
2	14	14
3	12	14

end0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample1.1s (26.9%)

Algorithm

1×

intervals

Results

270.0ms	4468×	body	128	valid
242.0ms	1292×	body	1024	valid
229.0ms	1498×	body	512	valid
124.0ms	742×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 119 to 88 computations (26.1% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze8.0ms (0.2%)

sample53.0ms (1.3%)

simplify14.0ms (0.3%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series13.0ms (0.3%)

rewrite182.0ms (4.3%)

simplify405.0ms (9.6%)

prune896.0ms (21.3%)

localize8.0ms (0.2%)

series6.0ms (0.2%)

rewrite48.0ms (1.1%)

simplify73.0ms (1.7%)

prune192.0ms (4.6%)

localize12.0ms (0.3%)

series8.0ms (0.2%)

rewrite53.0ms (1.3%)

simplify100.0ms (2.4%)

prune295.0ms (7%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite11.0ms (0.3%)

simplify66.0ms (1.6%)

prune188.0ms (4.5%)

regimes427.0ms (10.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (26.9%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22