Details

analyze1.3s (15.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.8%	89.9%	0.2%	11
14.1%	85.7%	0.2%	12
22.6%	77.1%	0.2%	13
23.7%	76%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample31.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	211×	body	128	valid
3.0ms	15×	body	1024	valid
2.0ms	14×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	22×	body	128	invalid
0.0ms	2×	body	2048	valid

Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify138.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune3.0ms (0%)

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

11.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.6b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.6b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	2.9b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 88

Calls

2 calls:

15.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
8.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series104.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

78.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
26.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

636×	`cancel-sign-sub-inv_binary64`
413×	`sub-neg_binary64`
250×	`fma-neg_binary64`
179×	`+-commutative_binary64`
175×	`times-frac_binary64`

Counts

184 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	4391
1	829	4287
2	3165	4222
3	5014	4222

prune136.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	284	8	292
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	286	8	294

Error

0.9b

Counts

294 → 8

Alt Table

Status	Error	Program
	11.7b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (-.f64 a t))) (+.f64 x y))
	14.3b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	11.9b	(fma.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 t z)))) (+.f64 x y))
	28.9b	x
	37.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
▶	11.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	11.6b	(+.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y)
	26.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))

Compiler

Compiled 4558 to 1333 computations (70.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.3b	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
✓	3.8b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 133

Calls

3 calls:

19.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
15.0ms	(/.f64 1 (-.f64 a t))
9.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

series139.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

74.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
51.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
13.0ms	(/.f64 1 (-.f64 a t))

simplify237.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

684×	`cancel-sign-sub-inv_binary64`
413×	`sub-neg_binary64`
294×	`fma-neg_binary64`
191×	`+-commutative_binary64`
180×	`times-frac_binary64`

Counts

253 → 424

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	5255
1	898	5010
2	3430	4935
3	5609	4935

prune430.0ms (5.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	423	1	424
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	423	9	432

Error

0.9b

Counts

432 → 9

Alt Table

Status	Error	Program
	11.7b	(fma.f64 y (/.f64 (/.f64 (-.f64 t z) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (-.f64 a t))) (+.f64 x y))
	14.3b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	11.9b	(fma.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 t z)))) (+.f64 x y))
	28.9b	x
	37.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	51.3b	(sqrt.f64 (.f64 (fma.f64 y (.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y)) (fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))))
✓	11.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
▶	11.6b	(+.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y)
	26.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))

Compiler

Compiled 6466 to 2338 computations (63.8% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	0.5b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)
✓	2.3b	(+.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y)

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-cube-cbrt_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
8×	`fma-udef_binary64`

Counts

2 → 76

Calls

2 calls:

24.0ms	(+.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y)
19.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)

series284.0ms (3.4%)

Counts

2 → 120

Calls

2 calls:

149.0ms	(+.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x) y)
135.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)

simplify302.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

686×	`cancel-sign-sub-inv_binary64`
606×	`fma-neg_binary64`
447×	`distribute-rgt-in_binary64`
394×	`sub-neg_binary64`
177×	`associate--l+_binary64`

Counts

196 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	5209
1	682	5174
2	2696	4108
3	4840	4108
4	5095	4108

prune399.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	470	4	474
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	475	8	483

Error

0.0b

Counts

483 → 8

Alt Table

Status	Error	Program
▶	11.6b	(+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))
	41.1b	(-.f64 (+.f64 (+.f64 x (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 a z) t)))) (.f64 (/.f64 y (pow.f64 t 3)) (-.f64 (.f64 a (.f64 a z)) (pow.f64 a 3)))) (.f64 (/.f64 y t) (+.f64 a (/.f64 (*.f64 a a) t))))
✓	11.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	14.3b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	11.9b	(fma.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 t z)))) (+.f64 x y))
	27.4b	(+.f64 (/.f64 (.f64 y z) t) (+.f64 x (.f64 (/.f64 a t) (-.f64 (/.f64 (*.f64 y z) t) y))))
	24.5b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	26.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))

Compiler

Compiled 7121 to 2010 computations (71.8% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
	0.5b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x)
✓	2.3b	(+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`flip3-+_binary64`
4×	`pow1_binary64`

Counts

1 → 43

Calls

1 calls:

26.0ms

(+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))

series140.0ms (1.7%)

Counts

1 → 60

Calls

1 calls:

140.0ms

(+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))

simplify173.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
426×	`cancel-sign-sub-inv_binary64`
324×	`distribute-rgt-in_binary64`
284×	`distribute-lft-in_binary64`
224×	`associate-/l/_binary64`

Counts

103 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2824
1	488	2783
2	2214	2299
3	4576	2245
4	5150	2245

prune375.0ms (4.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	601	0	601
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	601	8	609

Error

0.0b

Counts

609 → 8

Alt Table

Status	Error	Program
✓	11.6b	(+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))
	41.1b	(-.f64 (+.f64 (+.f64 x (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 a z) t)))) (.f64 (/.f64 y (pow.f64 t 3)) (-.f64 (.f64 a (.f64 a z)) (pow.f64 a 3)))) (.f64 (/.f64 y t) (+.f64 a (/.f64 (*.f64 a a) t))))
✓	11.6b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	14.3b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 y t) (-.f64 a t)) x)) (/.f64 (.f64 y z) (-.f64 a t)))
	11.9b	(fma.f64 y (/.f64 (*.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z))) (/.f64 (-.f64 a t) (cbrt.f64 (-.f64 t z)))) (+.f64 x y))
	27.4b	(+.f64 (/.f64 (.f64 y z) t) (+.f64 x (.f64 (/.f64 a t) (-.f64 (/.f64 (*.f64 y z) t) y))))
	24.5b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	26.2b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))

Compiler

Compiled 6610 to 1900 computations (71.3% saved)

regimes1.9s (22.9%)

Accuracy

Total 5.0b remaining (98.4%)

Threshold costs 0b (0%)

Compiler

Compiled 14832 to 9138 computations (38.4% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
13×	`*-commutative_binary64`
13×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	112
1	52	112
2	68	112
3	83	112
4	94	112
5	106	112
6	113	112
7	119	112
8	125	112
9	128	112
10	129	112
11	125	112

end2.0ms (0%)

Compiler: Compiled 81 to 31 computations (61.7% saved)

sample1.9s (23%)

Algorithm

1×

intervals

Results

638.0ms	6757×	body	128	valid
134.0ms	355×	body	1024	valid
129.0ms	460×	body	512	valid
75.0ms	383×	body	256	valid
62.0ms	683×	body	128	invalid
19.0ms	45×	body	2048	valid

Compiler

Compiled 295 to 153 computations (48.1% saved)

Iter	Nodes	Cost
0	33	112
1	52	112
2	68	112
3	83	112
4	94	112
5	106	112
6	113	112
7	119	112
8	125	112
9	128	112
10	129	112
11	125	112

Iter	Nodes	Cost
0	33	112
1	52	112
2	68	112
3	83	112
4	94	112
5	106	112
6	113	112
7	119	112
8	125	112
9	128	112
10	129	112
11	125	112

Details

analyze1.3s (15.1%)

sample31.0ms (0.4%)

simplify138.0ms (1.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite30.0ms (0.4%)

series104.0ms (1.2%)

simplify130.0ms (1.6%)

prune136.0ms (1.6%)

localize10.0ms (0.1%)

rewrite48.0ms (0.6%)

series139.0ms (1.7%)

simplify237.0ms (2.8%)

prune430.0ms (5.1%)

localize17.0ms (0.2%)

rewrite50.0ms (0.6%)

series284.0ms (3.4%)

simplify302.0ms (3.6%)

prune399.0ms (4.8%)

localize16.0ms (0.2%)

rewrite31.0ms (0.4%)

series140.0ms (1.7%)

simplify173.0ms (2.1%)

prune375.0ms (4.5%)

regimes1.9s (22.9%)

bsearch9.0ms (0.1%)

simplify19.0ms (0.2%)

end2.0ms (0%)

sample1.9s (23%)

Profiling

Iter	Nodes	Cost
0	33	112
1	52	112
2	68	112
3	83	112
4	94	112
5	106	112
6	113	112
7	119	112
8	125	112
9	128	112
10	129	112
11	125	112