Details

analyze2.4s (8.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0.6%	99.1%	0.3%	11
1.8%	98%	0.3%	12
2.6%	97.1%	0.3%	13
4%	95.7%	0.3%	14

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample91.0ms (0.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify74.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
593×	`fma-def_binary64`
507×	`div-sub_binary64`
484×	`sub-neg_binary64`
470×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	25	21
2	50	21
3	93	21
4	157	21
5	270	21
6	423	21
7	724	21
8	1341	21
9	3898	21
10	4400	21
11	4952	21

prune3.0ms (0%)

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

22.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.2b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

Compiler

Compiled 80 to 41 computations (48.8% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 t a))
✓	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	21.6b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

series211.0ms (0.7%)

Counts

3 → 168

Calls

3 calls:

191.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
13.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))
6.0ms	(*.f64 z (-.f64 t a))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 89

Calls

3 calls:

7.0ms	(*.f64 z (-.f64 t a))
2.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
0.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))

simplify138.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

911×	`associate-/l*_binary64`
492×	`fma-def_binary64`
259×	`+-commutative_binary64`
206×	`associate-+r+_binary64`
151×	`*-commutative_binary64`

Counts

257 → 217

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	765	9527
1	2314	8862
2	5234	8862

prune246.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	207	10	217
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	208	10	218

Error

0.0b

Counts

218 → 10

Alt Table

Status	Error	Program
	22.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	27.8b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	41.2b	(/.f64 (fma.f64 x y (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
	39.4b	(/.f64 (fma.f64 x y (cbrt.f64 (.f64 (.f64 (.f64 z (-.f64 t a)) (.f64 z (-.f64 t a))) (*.f64 z (-.f64 t a))))) (fma.f64 z (-.f64 b y) y))
	32.0b	(/.f64 (-.f64 t a) (-.f64 b y))
	31.9b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.5b	(/.f64 x (-.f64 1 z))
▶	22.3b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	29.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	22.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 z (-.f64 b y) y)) (cbrt.f64 (fma.f64 z (-.f64 b y) y)))) (/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (cbrt.f64 (fma.f64 z (-.f64 b y) y))))

Compiler

Compiled 11415 to 4350 computations (61.9% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	0.7b	(/.f64 1 (fma.f64 z (-.f64 b y) y))
✓	21.0b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series216.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

175.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
41.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 71

Calls

2 calls:

5.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
2.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

simplify155.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

788×	`associate-/l*_binary64`
519×	`fma-def_binary64`
318×	`+-commutative_binary64`
239×	`associate-+r+_binary64`
177×	`sub-neg_binary64`

Counts

179 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	812	10485
1	2614	9766
2	5311	9766

prune306.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	321	2	323
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	323	10	333

Error

0.0b

Counts

333 → 10

Alt Table

Status	Error	Program
▶	22.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	27.8b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	41.2b	(/.f64 (fma.f64 x y (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (-.f64 t a)))) (fma.f64 z (-.f64 b y) y))
	39.4b	(/.f64 (fma.f64 x y (cbrt.f64 (.f64 (.f64 (.f64 z (-.f64 t a)) (.f64 z (-.f64 t a))) (*.f64 z (-.f64 t a))))) (fma.f64 z (-.f64 b y) y))
	32.0b	(/.f64 (-.f64 t a) (-.f64 b y))
	31.9b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.5b	(/.f64 x (-.f64 1 z))
	42.6b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))))
	22.4b	(.f64 (fma.f64 x y (+.f64 (.f64 z t) (.f64 z (.f64 (neg.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	29.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))

Compiler

Compiled 15574 to 6351 computations (59.2% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
	0.3b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
✓	21.6b	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

series575.0ms (2%)

Counts

2 → 144

Calls

2 calls:

388.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))
186.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
2.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

simplify232.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

656×	`+-commutative_binary64`
547×	`associate-+r+_binary64`
293×	`associate-/l*_binary64`
280×	`*-commutative_binary64`
202×	`associate-/r*_binary64`

Counts

251 → 304

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1525	24218
1	5092	24218

prune829.0ms (2.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	390	1	391
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	391	10	401

Error

0.0b

Counts

401 → 10

Alt Table

Status	Error	Program
	22.4b	(.f64 (fma.f64 x y (+.f64 (.f64 z t) (.f64 z (.f64 (neg.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
▶	22.2b	(+.f64 (/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y))) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y))))
✓	22.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	27.8b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	39.4b	(/.f64 (fma.f64 x y (cbrt.f64 (.f64 (.f64 (.f64 z (-.f64 t a)) (.f64 z (-.f64 t a))) (*.f64 z (-.f64 t a))))) (fma.f64 z (-.f64 b y) y))
	32.0b	(/.f64 (-.f64 t a) (-.f64 b y))
	31.9b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	43.5b	(/.f64 x (-.f64 1 z))
	42.6b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))))
	29.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))

Compiler

Compiled 29383 to 12219 computations (58.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z a))
✓	0.9b	(-.f64 (+.f64 (.f64 z b) y) (.f64 z y))
✓	13.3b	(/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y)))
✓	19.6b	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y)))

series198.0ms (0.7%)

Counts

4 → 192

Calls

4 calls:

114.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y)))
69.0ms	(/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y)))
8.0ms	(-.f64 (.f64 x y) (.f64 z a))
7.0ms	(-.f64 (+.f64 (.f64 z b) y) (.f64 z y))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 97

Calls

4 calls:

25.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y)))
7.0ms	(/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y)))
5.0ms	(-.f64 (+.f64 (.f64 z b) y) (.f64 z y))
3.0ms	(-.f64 (.f64 x y) (.f64 z a))

simplify208.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

873×	`times-frac_binary64`
455×	`fma-def_binary64`
208×	`+-commutative_binary64`
189×	`sub-neg_binary64`
158×	`associate-/l*_binary64`

Counts

289 → 319

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	749	9848
1	2320	9173
2	5001	9173

prune546.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	366	9	375

Error

0.0b

Counts

375 → 9

Alt Table

Status	Error	Program
✓	22.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	27.8b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	29.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))
	31.5b	(+.f64 (/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y))) (-.f64 (/.f64 x (-.f64 1 z)) (fma.f64 (/.f64 b y) (/.f64 (.f64 z x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 a z) (.f64 y (-.f64 1 z))))))
	39.4b	(/.f64 (fma.f64 x y (cbrt.f64 (.f64 (.f64 (.f64 z (-.f64 t a)) (.f64 z (-.f64 t a))) (*.f64 z (-.f64 t a))))) (fma.f64 z (-.f64 b y) y))
	32.0b	(/.f64 (-.f64 t a) (-.f64 b y))
	31.9b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 z (-.f64 1 z)) (/.f64 x (-.f64 1 z))) (fma.f64 (/.f64 z y) (/.f64 (.f64 b x) (pow.f64 (-.f64 1 z) 2)) (/.f64 (.f64 z a) (*.f64 y (-.f64 1 z)))))
	42.6b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (sqrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))))
	22.4b	(.f64 (fma.f64 x y (+.f64 (.f64 z t) (.f64 z (.f64 (neg.f64 (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

Compiler

Compiled 18919 to 4776 computations (74.8% saved)

regimes21.4s (73%)

Accuracy

Total 6.0b remaining (98.3%)

Threshold costs 0b (0%)

Counts

462 → 5

Compiler

Compiled 123511 to 68354 computations (44.7% saved)

bsearch108.0ms (0.4%)

Steps

Iters	Range		Point
8	93353622849.6066	856552822850550.0	95120340125.92792
9	4.637277625808953e-210	1.7930259029645583e-203	6.002196668933548e-210
8	-7.688038587470378e-278	-2.9706266962810924e-281	-3.910612387742409e-279
6	-3897895985894365.0	-330533886252231.8	-369640450397408.9

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

23×	`+-commutative_binary64`
20×	`*-commutative_binary64`
17×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	277
1	97	275
2	122	275
3	143	275
4	160	275
5	173	275
6	180	275
7	184	275
8	185	275
9	183	275

end2.0ms (0%)

Compiler: Compiled 194 to 71 computations (63.4% saved)

sample1.3s (4.3%)

Algorithm

1×

intervals

Results

475.0ms	8000×	body	128	valid
26.0ms	446×	body	128	invalid

Compiler

Compiled 548 to 270 computations (50.7% saved)

Iter	Nodes	Cost
0	66	277
1	97	275
2	122	275
3	143	275
4	160	275
5	173	275
6	180	275
7	184	275
8	185	275
9	183	275

Iter	Nodes	Cost
0	66	277
1	97	275
2	122	275
3	143	275
4	160	275
5	173	275
6	180	275
7	184	275
8	185	275
9	183	275

Details

analyze2.4s (8.1%)

sample91.0ms (0.3%)

simplify74.0ms (0.3%)

prune3.0ms (0%)

localize11.0ms (0%)

series211.0ms (0.7%)

rewrite15.0ms (0.1%)

simplify138.0ms (0.5%)

prune246.0ms (0.8%)

localize11.0ms (0%)

series216.0ms (0.7%)

rewrite12.0ms (0%)

simplify155.0ms (0.5%)

prune306.0ms (1%)

localize14.0ms (0%)

series575.0ms (2%)

rewrite23.0ms (0.1%)

simplify232.0ms (0.8%)

prune829.0ms (2.8%)

localize15.0ms (0.1%)

series198.0ms (0.7%)

rewrite45.0ms (0.2%)

simplify208.0ms (0.7%)

prune546.0ms (1.9%)

regimes21.4s (73%)

bsearch108.0ms (0.4%)

simplify15.0ms (0.1%)

end2.0ms (0%)

sample1.3s (4.3%)

Profiling

Iter	Nodes	Cost
0	66	277
1	97	275
2	122	275
3	143	275
4	160	275
5	173	275
6	180	275
7	184	275
8	185	275
9	183	275