Details

analyze230.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample25.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify217.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0.1%)

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

0.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.2b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite162.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

37×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

4 → 168

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
16.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
15.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
12.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 3394 to 2161 computations (36.3% saved)

series34.0ms (1.1%)

Error

0.0b

Counts

4 → 16

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
7.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
5.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

Compiler

Compiled 456 to 379 computations (16.9% saved)

simplify125.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-def_binary64`
541×	`associate-/r*_binary64`
412×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
202×	`associate-/l/_binary64`

Counts

184 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	3279
1	443	2899
2	1534	2627
3	4836	2627
4	4983	2627

prune40.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	62	3	65

Error

0.0b

Counts

65 → 3

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
	31.1b	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))
▶	0.2b	(-.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x)))

Compiler

Compiled 1159 to 748 computations (35.5% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(fma.f64 1/4 (*.f64 x x) (log.f64 x))
0.2b	(-.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x)))

rewrite88.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-cube-cbrt_binary64`
14×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`fma-udef_binary64`
6×	`add-cbrt-cube_binary64`

Counts

2 → 83

Calls

2 calls:

14.0ms	(-.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x)))
13.0ms	(fma.f64 1/4 (*.f64 x x) (log.f64 x))

Compiler

Compiled 2064 to 1100 computations (46.7% saved)

series30.0ms (1%)

Error

0.0b

Counts

2 → 10

Calls

2 calls:

14.0ms	(-.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x)))
13.0ms	(fma.f64 1/4 (*.f64 x x) (log.f64 x))

Compiler

Compiled 236 to 200 computations (15.3% saved)

simplify88.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

454×	`distribute-rgt-in_binary64`
447×	`associate-l_binary64`
404×	`distribute-lft-in_binary64`
379×	`fma-def_binary64`
373×	`associate-r_binary64`

Counts

93 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1513
1	271	1459
2	897	1418
3	4241	1391
4	4831	1391

prune28.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
	31.1b	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))
▶	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) 3)) (fma.f64 (log.f64 2) (log.f64 2) (.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (.f64 x x) (log.f64 x))))))

Compiler

Compiled 745 to 446 computations (40.1% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) 3)) (fma.f64 (log.f64 2) (log.f64 2) (.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (.f64 x x) (log.f64 x))))))
0.4b	(.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x))))
0.7b	(pow.f64 (fma.f64 1/4 (*.f64 x x) (log.f64 x)) 3)
1.0b	(pow.f64 (log.f64 2) 3)

rewrite263.0ms (8.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 189

Calls

4 calls:

19.0ms	(pow.f64 (log.f64 2) 3)
18.0ms	(.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x))))
16.0ms	(/.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) 3)) (fma.f64 (log.f64 2) (log.f64 2) (.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (.f64 x x) (log.f64 x))))))
13.0ms	(pow.f64 (fma.f64 1/4 (*.f64 x x) (log.f64 x)) 3)

Compiler

Compiled 7956 to 4878 computations (38.7% saved)

series113.0ms (3.8%)

Error

Counts

4 → 13

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) 3)) (fma.f64 (log.f64 2) (log.f64 2) (.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (.f64 x x) (log.f64 x))))))
12.0ms	(.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (*.f64 x x) (log.f64 x))))
11.0ms	(pow.f64 (fma.f64 1/4 (*.f64 x x) (log.f64 x)) 3)
0.0ms	(pow.f64 (log.f64 2) 3)

Compiler

Compiled 2196 to 1676 computations (23.7% saved)

simplify156.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

443×	`cancel-sign-sub-inv_binary64`
282×	`associate-l_binary64`
278×	`associate-r_binary64`
273×	`fma-neg_binary64`
126×	`fma-def_binary64`

Counts

202 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	6405
1	665	5772
2	3131	5620
3	4944	5620

prune103.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	124	3	127

Error

Counts

127 → 3

Alt Table

Status	Error	Program
✓	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	31.1b	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))
✓	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) 3)) (fma.f64 (log.f64 2) (log.f64 2) (.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (.f64 x x) (log.f64 x))))))

Compiler

Compiled 4698 to 2911 computations (38% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.2b	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))
28.7b	(/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x))

rewrite110.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 129

Calls

3 calls:

14.0ms	(/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x))
14.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
11.0ms	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))

Compiler

Compiled 2767 to 1379 computations (50.2% saved)

series22.0ms (0.7%)

Error

Counts

3 → 12

Calls

3 calls:

7.0ms	(/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x))
6.0ms	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))
5.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 339 to 257 computations (24.2% saved)

simplify109.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-l_binary64`
449×	`associate-/l*_binary64`
424×	`associate-r_binary64`
248×	`associate-/r*_binary64`
214×	`associate-*l/_binary64`

Counts

141 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2803
1	339	2420
2	1031	2180
3	4619	2174
4	4938	2174

prune28.0ms (0.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	50	3	53

Error

Counts

53 → 3

Alt Table

Status	Error	Program
	0.3b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
	31.1b	(log.f64 (/.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x)))
	0.5b	(/.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) 3)) (fma.f64 (log.f64 2) (log.f64 2) (.f64 (fma.f64 1/4 (.f64 x x) (log.f64 x)) (+.f64 (log.f64 2) (fma.f64 1/4 (.f64 x x) (log.f64 x))))))

Compiler

Compiled 953 to 523 computations (45.1% saved)

regimes150.0ms (5%)

Accuracy

Total 0.5b remaining (99.5%)

Threshold costs 0.5b (99.5%)

Compiler

Compiled 2109 to 1499 computations (28.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-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	9	15
1	11	15
2	16	15
3	18	15
4	19	15
5	19	15

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample832.0ms (27.7%)

Algorithm

1×

intervals

Results

567.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 95 to 64 computations (32.6% saved)

Details

analyze230.0ms (7.7%)

sample25.0ms (0.8%)

simplify217.0ms (7.2%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite162.0ms (5.4%)

series34.0ms (1.1%)

simplify125.0ms (4.2%)

prune40.0ms (1.3%)

localize8.0ms (0.3%)

rewrite88.0ms (2.9%)

series30.0ms (1%)

simplify88.0ms (2.9%)

prune28.0ms (0.9%)

localize16.0ms (0.5%)

rewrite263.0ms (8.8%)

series113.0ms (3.8%)

simplify156.0ms (5.2%)

prune103.0ms (3.4%)

localize10.0ms (0.3%)

rewrite110.0ms (3.7%)

series22.0ms (0.7%)

simplify109.0ms (3.6%)

prune28.0ms (0.9%)

regimes150.0ms (5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample832.0ms (27.7%)

Profiling