Details

analyze37.0ms (0.8%)

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)

sample34.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	35×	body	1024	valid
7.0ms	148×	body	128	valid
6.0ms	43×	body	512	valid
3.0ms	30×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify19.0ms (0.4%)

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 → 1

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

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

10.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 48 to 39 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.6b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite289.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

9.7b

Rules

59×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-log-exp_binary64`
16×	`add-exp-log_binary64`

Counts

4 → 205

Calls

4 calls:

21.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
17.0ms	(/.f64 1 (+.f64 x 1))
17.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
15.0ms	(/.f64 1 (-.f64 x 1))

Compiler

Compiled 4640 to 3800 computations (18.1% saved)

series73.0ms (1.6%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

14.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
14.0ms	(/.f64 1 (-.f64 x 1))
10.0ms	(/.f64 1 (+.f64 x 1))
9.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))

Compiler

Compiled 1486 to 1208 computations (18.7% saved)

simplify145.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

955×	`fma-neg_binary64`
517×	`cancel-sign-sub-inv_binary64`
167×	`fma-def_binary64`
161×	`sub-neg_binary64`
138×	`associate-r_binary64`

Counts

253 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	295	3727
1	763	3499
2	2806	3361
3	4663	3360
4	4845	3360

prune99.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	159	4	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	4	164

Error

0.0b

Counts

164 → 4

Alt Table

Status	Error	Program
	25.1b	(.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 x -1))))
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
	32.8b	(+.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)))))
▶	10.3b	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))

Compiler

Compiled 2829 to 2222 computations (21.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (+.f64 x -1))
0.0b	(+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1)))
2.5b	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))

rewrite230.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

46×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`add-log-exp_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`

Counts

4 → 194

Calls

4 calls:

15.0ms	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))
14.0ms	(/.f64 1 (+.f64 x -1))
13.0ms	(+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1)))
13.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 3787 to 3103 computations (18.1% saved)

series66.0ms (1.5%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

14.0ms	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))
11.0ms	(+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1)))
9.0ms	(/.f64 1 (+.f64 x 1))
9.0ms	(/.f64 1 (+.f64 x -1))

Compiler

Compiled 1489 to 1211 computations (18.7% saved)

simplify138.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-neg_binary64`
403×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-neg-in_binary64`
158×	`fma-def_binary64`
154×	`distribute-neg-in_binary64`

Counts

242 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	3297
1	710	3115
2	2602	3097
3	4730	3097
4	5170	3097

prune65.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	119	4	123

Error

0.0b

Counts

123 → 4

Alt Table

Status	Error	Program
▶	25.1b	(.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 x -1))))
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
	32.8b	(+.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)))))
✓	10.3b	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))

Compiler

Compiled 1859 to 1426 computations (23.3% saved)

localize24.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (fma.f64 x x x) (+.f64 x -1))
0.1b	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 x -1)))
0.2b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
16.0b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite270.0ms (6.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-cube-cbrt_binary64`
25×	`pow1_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 195

Calls

4 calls:

24.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
22.0ms	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 x -1)))
18.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
17.0ms	(*.f64 (fma.f64 x x x) (+.f64 x -1))

Compiler

Compiled 7336 to 5204 computations (29.1% saved)

series57.0ms (1.3%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

21.0ms	(/.f64 1 (*.f64 (fma.f64 x x x) (+.f64 x -1)))
13.0ms	(*.f64 (fma.f64 x x x) (+.f64 x -1))
7.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
4.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

Compiler

Compiled 1421 to 1073 computations (24.5% saved)

simplify144.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
232×	`associate-l_binary64`
207×	`associate-r_binary64`
189×	`unswap-sqr_binary64`

Counts

222 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	4061
1	763	3429
2	2802	3330
3	4734	3329
4	4954	3329

prune125.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
	44.2b	(.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (cbrt.f64 (pow.f64 (/.f64 1 (*.f64 (+.f64 x -1) (fma.f64 x x x))) 3)))
	32.8b	(+.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)))))
✓	10.3b	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
▶	25.1b	(.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 (fma.f64 x x x) (/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3))))))

Compiler

Compiled 4612 to 3096 computations (32.9% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (fma.f64 x x x) (/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3))))
0.2b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
16.0b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
18.7b	(/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3)))

rewrite307.0ms (6.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

45×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-log-exp_binary64`

Counts

4 → 188

Calls

4 calls:

26.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
24.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
19.0ms	(/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3)))
13.0ms	(/.f64 (fma.f64 x x x) (/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3))))

Compiler

Compiled 8994 to 6150 computations (31.6% saved)

series65.0ms (1.5%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

21.0ms	(/.f64 (fma.f64 x x x) (/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3))))
16.0ms	(/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3)))
9.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
4.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

Compiler

Compiled 1719 to 1229 computations (28.5% saved)

simplify174.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-neg_binary64`
334×	`cancel-sign-sub-inv_binary64`
235×	`associate-l_binary64`
210×	`associate-r_binary64`
186×	`distribute-rgt-in_binary64`

Counts

215 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	276	4771
1	730	4105
2	3104	4000
3	4845	4000
4	5025	4000

prune130.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	120	5	125

Error

0.0b

Counts

125 → 5

Alt Table

Status	Error	Program
	44.2b	(.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (cbrt.f64 (pow.f64 (/.f64 1 (*.f64 (+.f64 x -1) (fma.f64 x x x))) 3)))
	32.8b	(+.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)))))
	10.3b	(+.f64 (/.f64 1 (+.f64 x 1)) (+.f64 (/.f64 -2 x) (/.f64 1 (+.f64 x -1))))
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
	25.1b	(.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (/.f64 1 (/.f64 (fma.f64 x x x) (/.f64 (+.f64 1 (fma.f64 x x x)) (+.f64 -1 (pow.f64 x 3))))))

Compiler

Compiled 4804 to 3108 computations (35.3% saved)

regimes787.0ms (17.8%)

Accuracy

Total 0.0b remaining (8.2%)

Threshold costs 0.0b (8.2%)

Compiler

Compiled 14926 to 11750 computations (21.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	15	17
2	14	17

end1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample1.1s (24.9%)

Algorithm

1×

intervals

Results

273.0ms	1336×	body	1024	valid
228.0ms	4417×	body	128	valid
221.0ms	1484×	body	512	valid
77.0ms	763×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 165 to 125 computations (24.2% 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

analyze37.0ms (0.8%)

sample34.0ms (0.8%)

simplify19.0ms (0.4%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite289.0ms (6.5%)

series73.0ms (1.6%)

simplify145.0ms (3.3%)

prune99.0ms (2.2%)

localize9.0ms (0.2%)

rewrite230.0ms (5.2%)

series66.0ms (1.5%)

simplify138.0ms (3.1%)

prune65.0ms (1.5%)

localize24.0ms (0.6%)

rewrite270.0ms (6.1%)

series57.0ms (1.3%)

simplify144.0ms (3.2%)

prune125.0ms (2.8%)

localize22.0ms (0.5%)

rewrite307.0ms (6.9%)

series65.0ms (1.5%)

simplify174.0ms (3.9%)

prune130.0ms (2.9%)

regimes787.0ms (17.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (24.9%)

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