Details

analyze1.8s (20.6%)

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
5.8%	93.9%	0.3%	11
8.4%	91.3%	0.3%	12
9.7%	90%	0.3%	13
10.7%	89%	0.3%	14

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample32.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	41	21
3	51	21
4	61	21
5	65	21
6	64	21

prune6.0ms (0.1%)

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

12.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.3b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	16.9b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 b (/.f64 y t) a)
✓	3.0b	(fma.f64 y (/.f64 z t) x)
✓	12.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series250.0ms (2.9%)

Counts

3 → 168

Calls

3 calls:

221.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
16.0ms	(fma.f64 b (/.f64 y t) a)
13.0ms	(fma.f64 y (/.f64 z t) x)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

4.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
0.0ms	(fma.f64 y (/.f64 z t) x)
0.0ms	(fma.f64 b (/.f64 y t) a)

simplify142.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

741×	`times-frac_binary64`
527×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
231×	`fma-def_binary64`
204×	`associate-l_binary64`

Counts

223 → 131

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	430	9216
1	1356	8684
2	4993	8684

prune219.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

0.0b

Counts

133 → 10

Alt Table

Status	Error	Program
	17.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.1b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) 3))
	42.2b	(/.f64 z b)
	38.4b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (fma.f64 b (/.f64 y t) 1)) (/.f64 x (fma.f64 b (/.f64 y t) 1))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 b (/.f64 y t) 1) 2))))
	15.5b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	38.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	40.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	16.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	16.6b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
▶	15.3b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 8166 to 3796 computations (53.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.3b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	6.3b	(/.f64 (*.f64 y b) t)
✓	6.9b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	11.4b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series301.0ms (3.5%)

Counts

4 → 152

Calls

4 calls:

143.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
125.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
20.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
13.0ms	(/.f64 (*.f64 y b) t)

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
25×	`add-cbrt-cube_binary64`
25×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`

Counts

4 → 111

Calls

4 calls:

10.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
9.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
8.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
3.0ms	(/.f64 (*.f64 y b) t)

simplify203.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/l*_binary64`
522×	`associate-/r*_binary64`
472×	`fma-def_binary64`
298×	`associate-l_binary64`
156×	`associate-*l/_binary64`

Counts

263 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	10630
1	1368	9571
2	4935	9243
3	5254	9243

prune302.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	266	3	269
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	269	10	279

Error

0.0b

Counts

279 → 10

Alt Table

Status	Error	Program
	38.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	28.2b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.6b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.1b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) 3))
▶	15.5b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	16.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	16.6b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	17.5b	(+.f64 (/.f64 (.f64 (/.f64 y (+.f64 1 (fma.f64 (/.f64 y t) b a))) z) t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 11953 to 4584 computations (61.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
	1.5b	(fma.f64 b (/.f64 y t) a)
✓	3.3b	(/.f64 (*.f64 y z) t)
✓	12.4b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series250.0ms (2.9%)

Counts

3 → 84

Calls

3 calls:

224.0ms	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
13.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
13.0ms	(/.f64 (*.f64 y z) t)

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

3 → 86

Calls

3 calls:

11.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
9.0ms	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
4.0ms	(/.f64 (*.f64 y z) t)

simplify129.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

790×	`times-frac_binary64`
574×	`associate-/l*_binary64`
418×	`associate-/r*_binary64`
244×	`fma-def_binary64`
143×	`+-commutative_binary64`

Counts

170 → 177

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	475	9245
1	1508	8739
2	5165	8739

prune216.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Error

0.0b

Counts

203 → 10

Alt Table

Status	Error	Program
	38.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	28.2b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.6b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.1b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) 3))
✓	15.5b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.8b	(-.f64 (+.f64 (/.f64 z b) (/.f64 (.f64 t x) (.f64 y b))) (+.f64 (/.f64 (.f64 t z) (.f64 y (pow.f64 b 2))) (/.f64 (.f64 a (.f64 t z)) (*.f64 y (pow.f64 b 2)))))
	16.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
▶	16.6b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	17.5b	(+.f64 (/.f64 (.f64 (/.f64 y (+.f64 1 (fma.f64 (/.f64 y t) b a))) z) t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 9863 to 4214 computations (57.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.5b	(fma.f64 b (/.f64 y t) a)
✓	3.3b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	5.7b	(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	10.7b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series485.0ms (5.7%)

Counts

3 → 180

Calls

3 calls:

288.0ms

(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

120.0ms

(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))

77.0ms

(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
8×	`associate-/r*_binary64`

Counts

3 → 80

Calls

3 calls:

3.0ms

(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))

3.0ms

(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))

0.0ms

(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))

simplify212.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/l*_binary64`
534×	`associate-/r*_binary64`
290×	`fma-def_binary64`
175×	`+-commutative_binary64`
162×	`associate-*l/_binary64`

Counts

260 → 202

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	560	16227
1	1790	15272
2	5036	15272

prune285.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	235	9	244

Error

Counts

244 → 9

Alt Table

Status	Error	Program
	38.7b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (/.f64 (.f64 a (.f64 z t)) (.f64 y (*.f64 b b)))))
	16.6b	(+.f64 (/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	17.2b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.1b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a))) 3))
✓	15.5b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	37.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	16.8b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
✓	16.6b	(fma.f64 (/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a))) (/.f64 z t) (/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	17.5b	(+.f64 (/.f64 (.f64 (/.f64 y (+.f64 1 (fma.f64 (/.f64 y t) b a))) z) t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

Compiler

Compiled 13156 to 5875 computations (55.3% saved)

regimes2.4s (28.1%)

Accuracy

Total 9.4b remaining (98.2%)

Threshold costs 0b (0%)

Counts

129 → 6

Compiler

Compiled 29135 to 17215 computations (40.9% saved)

bsearch88.0ms (1%)

Steps

Iters	Range		Point
11	6.0233233440562015e+221	1.7152754033907904e+241	6.194405303028895e+221
8	1.0986976529826878e-13	1.2025291994105397e-9	1.081035654397059e-9
5	-2.1630141904364737e+169	-8.466954377092181e+168	-1.884688025365851e+169
5	-1.364350235594205e+227	-6.349203709077036e+226	-1.0875447241440656e+227
2	-6.658706634147768e+276	-5.884922542116885e+276	-5.981645553620746e+276

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	191
1	61	191
2	60	191

end1.0ms (0%)

Compiler: Compiled 138 to 64 computations (53.6% saved)

sample1.1s (13%)

Algorithm

1×

intervals

Results

548.0ms	8000×	body	128	valid
17.0ms	278×	body	128	invalid

Compiler

Compiled 422 to 229 computations (45.7% saved)

Details

analyze1.8s (20.6%)

sample32.0ms (0.4%)

simplify8.0ms (0.1%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

series250.0ms (2.9%)

rewrite7.0ms (0.1%)

simplify142.0ms (1.7%)

prune219.0ms (2.6%)

localize14.0ms (0.2%)

series301.0ms (3.5%)

rewrite37.0ms (0.4%)

simplify203.0ms (2.4%)

prune302.0ms (3.5%)

localize16.0ms (0.2%)

series250.0ms (2.9%)

rewrite28.0ms (0.3%)

simplify129.0ms (1.5%)

prune216.0ms (2.5%)

localize12.0ms (0.1%)

series485.0ms (5.7%)

rewrite13.0ms (0.2%)

simplify212.0ms (2.5%)

prune285.0ms (3.3%)

regimes2.4s (28.1%)

bsearch88.0ms (1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (13%)

Profiling