Details

analyze10.0ms (0.3%)

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
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

Compiler

Compiled 175 to 47 computations (73.1% saved)

sample124.0ms (4.2%)

Algorithm

1×

intervals

Results

40.0ms

256×

body

128

valid

Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify67.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

755×	`unswap-sqr_binary64`
705×	`fma-def_binary64`
691×	`distribute-rgt-out_binary64`
576×	`+-commutative_binary64`
488×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	256
1	133	150
2	549	101
3	2427	90
4	3705	84
5	4529	84
6	4874	84
7	5887	84

prune9.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

28.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.9b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
	28.9b	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)

Status

Error

Program

▶

28.9b

(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

28.9b

(*.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 1049934947/10000000000 (*.f64 x x))) (*.f64 106015151/2500000000 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 36322091/5000000000 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 2532017/5000000000 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 1789971/10000000000 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 7715471019/10000000000 (*.f64 x x))) (*.f64 2909738639/10000000000 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 694555761/10000000000 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 70002721/5000000000 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 1665589/2000000000 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 (*.f64 2 1789971/10000000000) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x))))) x)

Compiler

Compiled 704 to 274 computations (61.1% saved)

localize30.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
✓	0.1b	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
✓	15.5b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
✓	28.4b	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))

series18.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))
6.0ms	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
3.0ms	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
2.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
2.0ms	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))
0.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
0.0ms	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))

simplify187.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-l_binary64`
498×	`associate-r_binary64`
321×	`fma-def_binary64`
247×	`distribute-rgt-in_binary64`
243×	`distribute-lft-in_binary64`

Counts

131 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	8073
1	443	7191
2	1315	7182
3	4848	7182
4	4920	7182

prune351.0ms (11.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	180	2	182

Error

Counts

182 → 2

Alt Table

Status	Error	Program
▶	31.3b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
	32.1b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Status

Error

Program

▶

31.3b

(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))

32.1b

(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 14412 to 10707 computations (25.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x)
✓	0.0b	(fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7)))
✓	0.1b	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))
✓	24.0b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))

series17.0ms (0.6%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7)))
5.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))
4.0ms	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
3.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))
3.0ms	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
0.0ms	(fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7)))
0.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x)

simplify115.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-neg_binary64`
633×	`times-frac_binary64`
600×	`associate-r_binary64`
389×	`fma-def_binary64`
339×	`distribute-lft-in_binary64`

Counts

115 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2229
1	264	2018
2	793	1831
3	3426	1774
4	4426	1759
5	5632	1759

prune102.0ms (3.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	122	2	124

Error

Counts

124 → 2

Alt Table

Status	Error	Program
✓	31.3b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
▶	32.1b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Status

Error

Program

✓

31.3b

(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))

▶

32.1b

(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 3472 to 2755 computations (20.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 600041/2386628 (pow.f64 x 3))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(/.f64 600041/2386628 (pow.f64 x 3))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
12×	`associate-/r*_binary64`

Counts

1 → 67

Calls

1 calls:

4.0ms

(/.f64 600041/2386628 (pow.f64 x 3))

simplify90.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

625×	`associate-/r*_binary64`
441×	`fma-def_binary64`
393×	`times-frac_binary64`
368×	`associate-l_binary64`
295×	`log-prod_binary64`

Counts

67 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	886
1	146	856
2	529	856
3	3175	800
4	4261	800
5	4973	800
6	4947	800

prune36.0ms (1.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	67	2	69

Error

Counts

69 → 2

Alt Table

Status	Error	Program
✓	31.3b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
✓	32.1b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Status

Error

Program

✓

31.3b

(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))

✓

32.1b

(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 1108 to 872 computations (21.3% saved)

regimes107.0ms (3.6%)

Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0.0b (-0.1%)

Counts

23 → 3

Compiler

Compiled 1308 to 650 computations (50.3% saved)

bsearch76.0ms (2.6%)

Steps

Iters	Range		Point
9	0.0001862608569235263	48114.428821313435	1.1600007318774805
10	-1234358720917023.5	-0.0164413197457152	-1.1547011278383645

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	49
1	30	49
2	30	49

end1.0ms (0%)

Compiler: Compiled 35 to 27 computations (22.9% saved)

sample1.6s (52.7%)

Algorithm

1×

intervals

Results

1.3s

8000×

body

128

valid

Compiler

Compiled 239 to 97 computations (59.4% saved)

Details

analyze10.0ms (0.3%)

sample124.0ms (4.2%)

simplify67.0ms (2.3%)

prune9.0ms (0.3%)

localize30.0ms (1%)

series18.0ms (0.6%)

rewrite18.0ms (0.6%)

simplify187.0ms (6.3%)

prune351.0ms (11.9%)

localize10.0ms (0.3%)

series17.0ms (0.6%)

rewrite12.0ms (0.4%)

simplify115.0ms (3.9%)

prune102.0ms (3.5%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite9.0ms (0.3%)

simplify90.0ms (3.1%)

prune36.0ms (1.2%)

regimes107.0ms (3.6%)

bsearch76.0ms (2.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.6s (52.7%)

Profiling