Details

analyze11.0ms (0.4%)

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 (3.9%)

Algorithm

1×

intervals

Results

43.0ms

256×

body

128

valid

Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify67.0ms (2.1%)

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

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

31.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.1b	(.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))))))))

Status

Error

Program

▶

31.1b

(*.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))))))))

Compiler

Compiled 356 to 182 computations (48.9% saved)

localize33.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
✓	0.2b	(fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1)))
✓	12.6b	(.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))))))))
✓	30.6b	(/.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)))))))

series172.0ms (5.4%)

Counts

4 → 48

Calls

4 calls:

160.0ms	(.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))))))))
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)))))))
4.0ms	(fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1)))
2.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)

rewrite19.0ms (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:

5.0ms	(.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 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1)))
0.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)

simplify201.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

546×	`associate-l_binary64`
479×	`associate-r_binary64`
363×	`fma-def_binary64`
243×	`distribute-rgt-in_binary64`
239×	`distribute-lft-in_binary64`

Counts

131 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	8196
1	456	7294
2	1329	7285
3	4916	7285
4	4959	7285

prune382.0ms (12%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	2	189

Error

Counts

189 → 2

Alt Table

Status	Error	Program
	31.9b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
▶	31.3b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 14930 to 11091 computations (25.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	0.2b	(/.f64 600041/2386628 (pow.f64 x 3))

series8.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

5.0ms	(/.f64 600041/2386628 (pow.f64 x 3))
3.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 96

Calls

2 calls:

22.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
4.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-l_binary64`
353×	`associate-/l*_binary64`
342×	`associate-*r/_binary64`
342×	`associate-*l/_binary64`
272×	`associate-/l/_binary64`

Counts

108 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1319
1	242	1280
2	965	1242
3	4706	1242
4	4947	1242

prune59.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Error

Counts

114 → 2

Alt Table

Status	Error	Program
▶	31.9b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
✓	31.3b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 1855 to 1438 computations (22.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓	19.5b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))

series10.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
3.0ms	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
0.0ms	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-l_binary64`
579×	`associate-r_binary64`
425×	`distribute-rgt-neg-out_binary64`
409×	`distribute-lft-in_binary64`
409×	`distribute-rgt-in_binary64`

Counts

44 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	602
1	67	518
2	148	518
3	590	518
4	3378	518
5	5281	518

prune23.0ms (0.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	38	2	40

Error

Counts

40 → 2

Alt Table

Status	Error	Program
✓	31.9b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
✓	31.3b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 603 to 460 computations (23.7% saved)

regimes81.0ms (2.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

17 → 3

Compiler

Compiled 1122 to 506 computations (54.9% saved)

bsearch85.0ms (2.7%)

Steps

Iters	Range		Point
11	0.00041998910911979074	3.763646979392097e+31	1.0899711136665788
10	-800967.5108152794	-1.5672234394412066e-6	-1.1045250954314907

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	22	42
1	26	42
2	26	42

end1.0ms (0%)

Compiler: Compiled 30 to 23 computations (23.3% saved)

sample1.7s (53.9%)

Algorithm

1×

intervals

Results

1.5s

8000×

body

128

valid

Compiler

Compiled 228 to 88 computations (61.4% saved)

Details

analyze11.0ms (0.4%)

sample124.0ms (3.9%)

simplify67.0ms (2.1%)

prune6.0ms (0.2%)

localize33.0ms (1%)

series172.0ms (5.4%)

rewrite19.0ms (0.6%)

simplify201.0ms (6.3%)

prune382.0ms (12%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite31.0ms (1%)

simplify76.0ms (2.4%)

prune59.0ms (1.8%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite1.0ms (0%)

simplify57.0ms (1.8%)

prune23.0ms (0.7%)

regimes81.0ms (2.5%)

bsearch85.0ms (2.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (53.9%)

Profiling