Details

analyze2.7s (19.2%)

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)

sample52.0ms (0.4%)

Algorithm

1×

intervals

Results

31.0ms	256×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify15.0ms (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

prune8.0ms (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

10.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.9b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
▶	14.3b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

Compiler

Compiled 126 to 78 computations (38.1% saved)

localize76.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 b (/.f64 y t) a))
✓	1.7b	(fma.f64 b (/.f64 y t) a)
✓	3.9b	(fma.f64 y (/.f64 z t) x)
✓	10.0b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series535.0ms (3.8%)

Counts

4 → 216

Calls

4 calls:

454.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
28.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
27.0ms	(fma.f64 b (/.f64 y t) a)
25.0ms	(fma.f64 y (/.f64 z t) x)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 73

Calls

4 calls:

7.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
6.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
1.0ms	(fma.f64 y (/.f64 z t) x)
1.0ms	(fma.f64 b (/.f64 y t) a)

simplify231.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

289 → 158

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	440	9932
1	1379	9371
2	5036	9371

prune350.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	148	10	158
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	10	160

Error

0.0b

Counts

160 → 10

Alt Table

Status	Error	Program
	31.0b	(.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (-.f64 1 (.f64 (fma.f64 b (/.f64 y t) a) (fma.f64 b (/.f64 y t) a)))) (-.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	13.0b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	42.8b	(-.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)))))
	37.7b	(-.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))))
	43.7b	(/.f64 z b)
	14.5b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (fma.f64 y (/.f64 z t) x)))
	49.4b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	32.1b	(-.f64 (fma.f64 (/.f64 y (+.f64 1 a)) (/.f64 z t) (/.f64 x (+.f64 1 a))) (/.f64 (.f64 y (.f64 x b)) (*.f64 t (pow.f64 (+.f64 1 a) 2))))
	13.3b	(+.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)))))
	41.4b	(-.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)))))

Compiler

Compiled 8768 to 3977 computations (54.6% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (fma.f64 b (/.f64 y t) a))
	1.7b	(fma.f64 b (/.f64 y t) a)
✓	5.2b	(/.f64 (*.f64 y z) t)
✓	10.0b	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series435.0ms (3.1%)

Counts

2 → 72

Calls

2 calls:

421.0ms	(/.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
14.0ms	(/.f64 (*.f64 y z) t)

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

2 → 65

Calls

2 calls:

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

simplify202.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

790×	`times-frac_binary64`
574×	`associate-/l*_binary64`
420×	`associate-/r*_binary64`
237×	`fma-def_binary64`
143×	`associate-*l/_binary64`

Counts

137 → 148

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	466	8993
1	1483	8475
2	5128	8475

prune362.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	186	5	191
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	191	10	201

Error

0.0b

Counts

201 → 10

Alt Table

Status	Error	Program
	49.4b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	16.1b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	13.1b	(.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	43.7b	(/.f64 z b)
	14.3b	(/.f64 (+.f64 (*.f64 (/.f64 y 1) (/.f64 z t)) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.1b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (+.f64 (/.f64 (*.f64 y z) t) x)))
	13.3b	(+.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)))))
▶	13.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 t (*.f64 y z))) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	31.0b	(.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (-.f64 1 (.f64 (fma.f64 b (/.f64 y t) a) (fma.f64 b (/.f64 y t) a)))) (-.f64 1 (fma.f64 b (/.f64 y t) a)))
	41.4b	(-.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)))))

Compiler

Compiled 9792 to 4234 computations (56.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (/.f64 t (*.f64 y z)))
	1.7b	(fma.f64 b (/.f64 y t) a)
✓	5.3b	(/.f64 t (*.f64 y z))
✓	10.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 t (*.f64 y z))) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series382.0ms (2.7%)

Counts

3 → 108

Calls

3 calls:

333.0ms	(/.f64 (+.f64 (/.f64 1 (/.f64 t (*.f64 y z))) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
27.0ms	(/.f64 t (*.f64 y z))
22.0ms	(/.f64 1 (/.f64 t (*.f64 y z)))

rewrite54.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
56×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 128

Calls

3 calls:

28.0ms	(/.f64 (+.f64 (/.f64 1 (/.f64 t (*.f64 y z))) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
7.0ms	(/.f64 t (*.f64 y z))
7.0ms	(/.f64 1 (/.f64 t (*.f64 y z)))

simplify239.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

837×	`times-frac_binary64`
601×	`associate-/l*_binary64`
466×	`associate-/r*_binary64`
238×	`fma-def_binary64`
143×	`+-commutative_binary64`

Counts

236 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	504	10430
1	1540	9598
2	5178	9598

prune577.0ms (4.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	252	0	252
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	252	10	262

Error

0.0b

Counts

262 → 10

Alt Table

Status	Error	Program
	49.4b	(*.f64 (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))) (/.f64 (sqrt.f64 (fma.f64 y (/.f64 z t) x)) (sqrt.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	16.1b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
▶	13.1b	(.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	43.7b	(/.f64 z b)
	14.3b	(/.f64 (+.f64 (*.f64 (/.f64 y 1) (/.f64 z t)) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.1b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (+.f64 (/.f64 (*.f64 y z) t) x)))
	13.3b	(+.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)))))
✓	13.0b	(/.f64 (+.f64 (/.f64 1 (/.f64 t (*.f64 y z))) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	31.0b	(.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (-.f64 1 (.f64 (fma.f64 b (/.f64 y t) a) (fma.f64 b (/.f64 y t) a)))) (-.f64 1 (fma.f64 b (/.f64 y t) a)))
	41.4b	(-.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)))))

Compiler

Compiled 11486 to 5151 computations (55.2% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	1.7b	(fma.f64 b (/.f64 y t) a)
	5.2b	(/.f64 (*.f64 y z) t)
✓	10.0b	(.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

series528.0ms (3.7%)

Counts

2 → 120

Calls

2 calls:

401.0ms	(.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
125.0ms	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))

rewrite51.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 87

Calls

2 calls:

27.0ms	(.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
9.0ms	(/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a)))

simplify367.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

663×	`associate-/l*_binary64`
536×	`associate-/r*_binary64`
287×	`fma-def_binary64`
169×	`+-commutative_binary64`
165×	`associate-*r/_binary64`

Counts

207 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	521	12625
1	1750	11807
2	5030	11807

prune452.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	247	1	248
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	249	9	258

Error

0.0b

Counts

258 → 9

Alt Table

Status	Error	Program
	36.0b	(.f64 (+.f64 (/.f64 (.f64 (/.f64 y (sqrt.f64 t)) z) (sqrt.f64 t)) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
✓	13.1b	(.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))
	16.1b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	43.7b	(/.f64 z b)
	14.3b	(/.f64 (+.f64 (*.f64 (/.f64 y 1) (/.f64 z t)) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	13.1b	(/.f64 1 (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (+.f64 (/.f64 (*.f64 y z) t) x)))
	13.3b	(+.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)))))
	31.0b	(.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (-.f64 1 (.f64 (fma.f64 b (/.f64 y t) a) (fma.f64 b (/.f64 y t) a)))) (-.f64 1 (fma.f64 b (/.f64 y t) a)))
	41.4b	(-.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)))))

Compiler

Compiled 12063 to 5423 computations (55% saved)

regimes4.4s (31.2%)

Accuracy

Total 6.8b remaining (95.1%)

Threshold costs 0b (0%)

Counts

158 → 3

Compiler

Compiled 33384 to 20828 computations (37.6% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 23 to 15 computations (34.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	125
1	44	125
2	43	125

end2.0ms (0%)

Compiler: Compiled 91 to 40 computations (56% saved)

sample2.0s (14.1%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
36.0ms	295×	body	128	invalid

Compiler

Compiled 369 to 205 computations (44.4% saved)

Details

analyze2.7s (19.2%)

sample52.0ms (0.4%)

simplify15.0ms (0.1%)

prune8.0ms (0.1%)

localize76.0ms (0.5%)

series535.0ms (3.8%)

rewrite18.0ms (0.1%)

simplify231.0ms (1.6%)

prune350.0ms (2.5%)

localize26.0ms (0.2%)

series435.0ms (3.1%)

rewrite19.0ms (0.1%)

simplify202.0ms (1.4%)

prune362.0ms (2.5%)

localize27.0ms (0.2%)

series382.0ms (2.7%)

rewrite54.0ms (0.4%)

simplify239.0ms (1.7%)

prune577.0ms (4.1%)

localize29.0ms (0.2%)

series528.0ms (3.7%)

rewrite51.0ms (0.4%)

simplify367.0ms (2.6%)

prune452.0ms (3.2%)

regimes4.4s (31.2%)

bsearch9.0ms (0.1%)

simplify5.0ms (0%)

end2.0ms (0%)

sample2.0s (14.1%)

Profiling