Details

analyze1.6s (20.4%)

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)

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify9.0ms (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

prune4.0ms (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

13.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	18.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	18.4b	(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	5.3b	(/.f64 (*.f64 y z) t)
✓	6.7b	(/.f64 (*.f64 y b) t)
✓	12.9b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series278.0ms (3.6%)

Counts

4 → 120

Calls

4 calls:

231.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
18.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
16.0ms	(/.f64 (*.f64 y b) t)
12.0ms	(/.f64 (*.f64 y z) t)

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
22×	`distribute-lft-out_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 112

Calls

4 calls:

10.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
4.0ms	(/.f64 (*.f64 y z) t)
4.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
3.0ms	(/.f64 (*.f64 y b) t)

simplify146.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

897×	`times-frac_binary64`
656×	`associate-/l*_binary64`
274×	`fma-def_binary64`
148×	`+-commutative_binary64`
118×	`distribute-rgt-in_binary64`

Counts

232 → 201

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	521	10152
1	1626	9540
2	5047	9540

prune248.0ms (3.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	192	9	201
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	193	10	203

Error

0.3b

Counts

203 → 10

Alt Table

Status	Error	Program
	19.6b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	41.7b	(/.f64 z b)
	45.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (fma.f64 (.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (.f64 b b)) (fma.f64 (/.f64 a y) (.f64 (/.f64 z b) (/.f64 t b)) (/.f64 (.f64 a (.f64 x (.f64 t t))) (.f64 (.f64 y b) (.f64 y b)))))))
	18.5b	(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)))))
▶	14.8b	(+.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)))))
	18.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.4b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	34.9b	(/.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (sqrt.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))) (sqrt.f64 (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))))
	18.3b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	18.4b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (/.f64 b t))))

Compiler

Compiled 10233 to 4395 computations (57.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.8b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	6.7b	(/.f64 (*.f64 y b) t)
✓	10.9b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series283.0ms (3.6%)

Counts

3 → 152

Calls

3 calls:

138.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
127.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
18.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`

Counts

3 → 88

Calls

3 calls:

8.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
8.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
7.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

simplify147.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

938×	`times-frac_binary64`
627×	`associate-/l*_binary64`
490×	`associate-/r*_binary64`
153×	`fma-def_binary64`
91×	`*-commutative_binary64`

Counts

240 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	395	10369
1	1285	9529
2	5042	9529

prune285.0ms (3.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	239	4	243
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	244	9	253

Error

0.2b

Counts

253 → 9

Alt Table

Status	Error	Program
	15.1b	(+.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)))))
	45.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (fma.f64 (.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (.f64 b b)) (fma.f64 (/.f64 a y) (.f64 (/.f64 z b) (/.f64 t b)) (/.f64 (.f64 a (.f64 x (.f64 t t))) (.f64 (.f64 y b) (.f64 y b)))))))
	18.5b	(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)))))
	15.7b	(+.f64 (/.f64 (/.f64 (.f64 y z) (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) t) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	18.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.4b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
▶	11.9b	(+.f64 (/.f64 (.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	18.4b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (/.f64 b t))))
	27.8b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))

Compiler

Compiled 11112 to 4381 computations (60.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 y b (fma.f64 a t t))
	2.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	6.7b	(/.f64 (*.f64 y b) t)
✓	10.9b	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

series138.0ms (1.8%)

Counts

2 → 108

Calls

2 calls:

128.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
10.0ms	(fma.f64 y b (fma.f64 a t t))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

3.0ms	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))
0.0ms	(fma.f64 y b (fma.f64 a t t))

simplify111.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

484×	`times-frac_binary64`
480×	`cancel-sign-sub-inv_binary64`
335×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`
211×	`fma-neg_binary64`

Counts

141 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	4826
1	717	4480
2	3716	4438
3	5080	4438

prune216.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Error

0.2b

Counts

212 → 8

Alt Table

Status	Error	Program
	45.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (fma.f64 (.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (.f64 b b)) (fma.f64 (/.f64 a y) (.f64 (/.f64 z b) (/.f64 t b)) (/.f64 (.f64 a (.f64 x (.f64 t t))) (.f64 (.f64 y b) (.f64 y b)))))))
	18.5b	(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)))))
	18.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	11.4b	(+.f64 (/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b))))))
	11.7b	(+.f64 (/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	11.9b	(+.f64 (.f64 (.f64 y z) (/.f64 1 (fma.f64 y b (fma.f64 a t t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	18.4b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (/.f64 b t))))
	27.8b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))

Compiler

Compiled 8735 to 3093 computations (64.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.8b	(fma.f64 y b (fma.f64 a t t))
✓	2.8b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b)))))
✓	5.4b	(/.f64 y (/.f64 t b))
	10.9b	(/.f64 (*.f64 y z) (fma.f64 y b (fma.f64 a t t)))

series169.0ms (2.2%)

Counts

2 → 96

Calls

2 calls:

157.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b)))))
12.0ms	(/.f64 y (/.f64 t b))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
74×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 111

Calls

2 calls:

16.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b)))))
4.0ms	(/.f64 y (/.f64 t b))

simplify199.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-def_binary64`
359×	`times-frac_binary64`
285×	`associate-/l*_binary64`
223×	`associate-/r*_binary64`
169×	`associate-/r/_binary64`

Counts

207 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	339	6305
1	915	5683
2	3856	5670
3	4822	5670
4	4997	5670
5	4973	5670

prune305.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	309	7	316

Error

0.2b

Counts

316 → 7

Alt Table

Status	Error	Program
	45.4b	(-.f64 (fma.f64 (/.f64 t y) (/.f64 x b) (/.f64 z b)) (fma.f64 (/.f64 t y) (/.f64 z (.f64 b b)) (fma.f64 (.f64 (/.f64 t y) (/.f64 t y)) (/.f64 x (.f64 b b)) (fma.f64 (/.f64 a y) (.f64 (/.f64 z b) (/.f64 t b)) (/.f64 (.f64 a (.f64 x (.f64 t t))) (.f64 (.f64 y b) (.f64 y b)))))))
	18.5b	(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)))))
	27.2b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 y (/.f64 t b))))))
	18.4b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	11.7b	(+.f64 (/.f64 y (/.f64 (fma.f64 y b (fma.f64 a t t)) z)) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	11.9b	(+.f64 (.f64 (.f64 y z) (/.f64 1 (fma.f64 y b (fma.f64 a t t)))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	18.4b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 y (/.f64 b t))))

Compiler

Compiled 11827 to 3783 computations (68% saved)

regimes2.4s (30.7%)

Accuracy

Total 4.7b remaining (88.4%)

Threshold costs 0b (0%)

Counts

126 → 4

Compiler

Compiled 30643 to 19157 computations (37.5% saved)

bsearch5.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	186
1	58	186
2	57	186

end1.0ms (0%)

Compiler: Compiled 133 to 56 computations (57.9% saved)

sample1.1s (13.8%)

Algorithm

1×

intervals

Results

547.0ms	8000×	body	128	valid
16.0ms	252×	body	128	invalid

Compiler

Compiled 385 to 200 computations (48.1% saved)

Details

analyze1.6s (20.4%)

sample30.0ms (0.4%)

simplify9.0ms (0.1%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

series278.0ms (3.6%)

rewrite28.0ms (0.4%)

simplify146.0ms (1.9%)

prune248.0ms (3.2%)

localize14.0ms (0.2%)

series283.0ms (3.6%)

rewrite30.0ms (0.4%)

simplify147.0ms (1.9%)

prune285.0ms (3.7%)

localize16.0ms (0.2%)

series138.0ms (1.8%)

rewrite5.0ms (0.1%)

simplify111.0ms (1.4%)

prune216.0ms (2.8%)

localize15.0ms (0.2%)

series169.0ms (2.2%)

rewrite31.0ms (0.4%)

simplify199.0ms (2.6%)

prune305.0ms (3.9%)

regimes2.4s (30.7%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (13.8%)

Profiling