Details

analyze26.0ms (1%)

Algorithm

1×

Search

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

6.0ms	59×	body	512	valid
5.0ms	148×	body	128	valid
3.0ms	40×	body	256	valid
1.0ms	9×	body	1024	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

16.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.3b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
4.1b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite250.0ms (9.4%)

Algorithm

1×	rewrite-expression-head

Error

15.2b

Rules

48×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`

Counts

3 → 154

Calls

3 calls:

18.0ms	(/.f64 1 (+.f64 x 1))
16.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
15.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 3123 to 2638 computations (15.5% saved)

series51.0ms (1.9%)

Error

0.4b

Counts

3 → 36

Calls

3 calls:

13.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
10.0ms	(/.f64 1 (-.f64 x 1))
10.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 970 to 804 computations (17.1% saved)

simplify110.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-neg_binary64`
329×	`cancel-sign-sub-inv_binary64`
286×	`distribute-rgt-in_binary64`
234×	`log-prod_binary64`
155×	`distribute-rgt-neg-in_binary64`

Counts

190 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2303
1	544	2173
2	2000	2149
3	4305	2149
4	4946	2149

prune67.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	4	123

Error

0.3b

Counts

123 → 4

Alt Table

Status	Error	Program
▶	15.8b	(/.f64 (+.f64 (-.f64 1 x) (+.f64 x 1)) (*.f64 (-.f64 1 x) (+.f64 x 1)))
	32.5b	(+.f64 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4))) (/.f64 -2 (pow.f64 x 6)))
	16.3b	(-.f64 (/.f64 -1 (-.f64 -1 x)) (/.f64 1 (-.f64 x 1)))
	16.3b	(/.f64 (+.f64 (/.f64 (+.f64 x -1) (+.f64 x 1)) -1) (-.f64 x 1))

Compiler

Compiled 1626 to 1308 computations (19.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 (-.f64 1 x) (+.f64 x 1)) (*.f64 (-.f64 1 x) (+.f64 x 1)))
0.0b	(*.f64 (-.f64 1 x) (+.f64 x 1))
3.6b	(+.f64 (-.f64 1 x) (+.f64 x 1))

rewrite187.0ms (7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

24×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
18×	`flip3--_binary64`
18×	`flip3-+_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 157

Calls

3 calls:

23.0ms	(/.f64 (+.f64 (-.f64 1 x) (+.f64 x 1)) (*.f64 (-.f64 1 x) (+.f64 x 1)))
20.0ms	(+.f64 (-.f64 1 x) (+.f64 x 1))
18.0ms	(*.f64 (-.f64 1 x) (+.f64 x 1))

Compiler

Compiled 3786 to 2850 computations (24.7% saved)

series34.0ms (1.3%)

Error

0.3b

Counts

3 → 21

Calls

3 calls:

13.0ms	(/.f64 (+.f64 (-.f64 1 x) (+.f64 x 1)) (*.f64 (-.f64 1 x) (+.f64 x 1)))
9.0ms	(*.f64 (-.f64 1 x) (+.f64 x 1))
3.0ms	(+.f64 (-.f64 1 x) (+.f64 x 1))

Compiler

Compiled 550 to 460 computations (16.4% saved)

simplify121.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-neg_binary64`
232×	`associate-l_binary64`
215×	`associate-r_binary64`
185×	`div-sub_binary64`
184×	`fma-def_binary64`

Counts

178 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	3123
1	710	2141
2	3320	2072
3	4759	2072
4	4811	2072

prune116.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	122	6	128

Error

Counts

128 → 6

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (/.f64 2 (+.f64 1 x)) (-.f64 1 x))
	20.9b	(/.f64 (.f64 (.f64 (-.f64 1 x) (+.f64 1 x)) 2) (pow.f64 (*.f64 (-.f64 1 x) (+.f64 1 x)) 2))
	8.2b	(.f64 (cbrt.f64 (/.f64 4 (pow.f64 (.f64 (-.f64 1 x) (+.f64 1 x)) 2))) (cbrt.f64 (/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))))
	1.1b	(/.f64 (.f64 (cbrt.f64 4) (cbrt.f64 2)) (.f64 (-.f64 1 x) (+.f64 x 1)))
	10.8b	(cbrt.f64 (/.f64 8 (pow.f64 (*.f64 (-.f64 1 x) (+.f64 1 x)) 3)))
	0.4b	(/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 2227 to 1664 computations (25.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 2 (+.f64 1 x))
0.1b	(/.f64 (/.f64 2 (+.f64 1 x)) (-.f64 1 x))

rewrite98.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
8×	`times-frac_binary64`
8×	`pow1_binary64`

Counts

2 → 96

Calls

2 calls:

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

Compiler

Compiled 1487 to 1221 computations (17.9% saved)

series47.0ms (1.8%)

Error

Counts

2 → 24

Calls

2 calls:

23.0ms	(/.f64 2 (+.f64 1 x))
12.0ms	(/.f64 (/.f64 2 (+.f64 1 x)) (-.f64 1 x))

Compiler

Compiled 682 to 578 computations (15.2% saved)

simplify87.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

541×	`associate-/l*_binary64`
517×	`associate-/r*_binary64`
463×	`fma-def_binary64`
283×	`fma-neg_binary64`
233×	`associate-/l/_binary64`

Counts

120 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1606
1	428	1480
2	1451	1452
3	4764	1448
4	5091	1448

prune55.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Error

Counts

89 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (+.f64 1 x)) (-.f64 1 x))
	20.9b	(/.f64 (.f64 (.f64 (-.f64 1 x) (+.f64 1 x)) 2) (pow.f64 (*.f64 (-.f64 1 x) (+.f64 1 x)) 2))
	8.2b	(.f64 (cbrt.f64 (/.f64 4 (pow.f64 (.f64 (-.f64 1 x) (+.f64 1 x)) 2))) (cbrt.f64 (/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))))
	1.1b	(/.f64 (.f64 (cbrt.f64 4) (cbrt.f64 2)) (.f64 (-.f64 1 x) (+.f64 x 1)))
	10.8b	(cbrt.f64 (/.f64 8 (pow.f64 (*.f64 (-.f64 1 x) (+.f64 1 x)) 3)))
▶	0.4b	(/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 1114 to 885 computations (20.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 (-.f64 1 x) (+.f64 1 x))
0.3b	(/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))

rewrite116.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`pow1_binary64`
15×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`

Counts

2 → 100

Calls

2 calls:

18.0ms	(*.f64 (-.f64 1 x) (+.f64 1 x))
18.0ms	(/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 1615 to 1289 computations (20.2% saved)

series28.0ms (1%)

Error

Counts

2 → 18

Calls

2 calls:

13.0ms	(/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))
8.0ms	(*.f64 (-.f64 1 x) (+.f64 1 x))

Compiler

Compiled 409 to 357 computations (12.7% saved)

simplify65.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
690×	`distribute-rgt-in_binary64`
502×	`times-frac_binary64`
165×	`fma-neg_binary64`
156×	`cancel-sign-sub-inv_binary64`

Counts

118 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1661
1	452	1487
2	1685	1462
3	5193	1462

prune48.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	84	5	89

Error

Counts

89 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f64 (/.f64 2 (+.f64 1 x)) (-.f64 1 x))
	20.9b	(/.f64 (.f64 (.f64 (-.f64 1 x) (+.f64 1 x)) 2) (pow.f64 (*.f64 (-.f64 1 x) (+.f64 1 x)) 2))
	8.2b	(.f64 (cbrt.f64 (/.f64 4 (pow.f64 (.f64 (-.f64 1 x) (+.f64 1 x)) 2))) (cbrt.f64 (/.f64 2 (*.f64 (-.f64 1 x) (+.f64 1 x)))))
	0.3b	(/.f64 2 (-.f64 1 (*.f64 x x)))
	1.1b	(/.f64 (.f64 (cbrt.f64 4) (cbrt.f64 2)) (.f64 (-.f64 1 x) (+.f64 x 1)))

Compiler

Compiled 1103 to 843 computations (23.6% saved)

regimes312.0ms (11.7%)

Accuracy

Total 0.1b remaining (80.4%)

Threshold costs 0.1b (80.4%)

Compiler

Compiled 5147 to 4287 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	13	13
2	17	13
3	19	13
4	20	13
5	19	13

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample775.0ms (29.1%)

Algorithm

1×

intervals

Results

210.0ms	1959×	body	512	valid
174.0ms	4566×	body	128	valid
78.0ms	1066×	body	256	valid
57.0ms	409×	body	1024	valid

Compiler

Compiled 100 to 82 computations (18% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Details

analyze26.0ms (1%)

sample22.0ms (0.8%)

simplify16.0ms (0.6%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

rewrite250.0ms (9.4%)

series51.0ms (1.9%)

simplify110.0ms (4.1%)

prune67.0ms (2.5%)

localize6.0ms (0.2%)

rewrite187.0ms (7%)

series34.0ms (1.3%)

simplify121.0ms (4.6%)

prune116.0ms (4.4%)

localize5.0ms (0.2%)

rewrite98.0ms (3.7%)

series47.0ms (1.8%)

simplify87.0ms (3.3%)

prune55.0ms (2.1%)

localize6.0ms (0.2%)

rewrite116.0ms (4.4%)

series28.0ms (1%)

simplify65.0ms (2.4%)

prune48.0ms (1.8%)

regimes312.0ms (11.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample775.0ms (29.1%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16