Details

analyze1.6s (16.6%)

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)

sample61.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	9×	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

prune4.0ms (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

10.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.1b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	13.8b	(/.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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))
✓	6.0b	(/.f64 (*.f64 y z) t)
✓	6.2b	(/.f64 (*.f64 y b) t)
✓	9.7b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series342.0ms (3.5%)

Counts

4 → 120

Calls

4 calls:

293.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
16.0ms	(/.f64 (*.f64 y z) t)
16.0ms	(/.f64 (*.f64 y b) t)
16.0ms	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

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

simplify155.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

897×	`times-frac_binary64`
657×	`associate-/l*_binary64`
275×	`fma-def_binary64`
148×	`+-commutative_binary64`
124×	`distribute-rgt-in_binary64`

Counts

238 → 218

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	527	10471
1	1638	9815
2	5071	9815

prune273.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	208	10	218
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	210	10	220

Error

0.0b

Counts

220 → 10

Alt Table

Status	Error	Program
	13.8b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	43.3b	(-.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)))))
	37.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))))
	46.3b	(/.f64 z b)
	14.6b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))) (cbrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t))))) (cbrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))))
	30.2b	(-.f64 (+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (.f64 y z) (.f64 (+.f64 1 a) t))) (/.f64 (.f64 y (.f64 b x)) (*.f64 (pow.f64 (+.f64 1 a) 2) t)))
	16.5b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
▶	13.3b	(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)))))
	34.1b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	14.2b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))

Compiler

Compiled 10753 to 4626 computations (57% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	3.7b	(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	6.2b	(/.f64 (*.f64 y b) t)
✓	7.4b	(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)))))

series554.0ms (5.7%)

Counts

3 → 168

Calls

3 calls:

354.0ms

(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)))))

121.0ms

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

79.0ms

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

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
24×	`distribute-lft-out_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`

Counts

3 → 88

Calls

3 calls:

7.0ms

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

6.0ms

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

0.0ms

(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)))))

simplify221.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/l*_binary64`
534×	`associate-/r*_binary64`
291×	`fma-def_binary64`
174×	`+-commutative_binary64`
163×	`associate-*l/_binary64`

Counts

256 → 200

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	556	16369
1	1787	15540
2	5113	15540

prune354.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	250	4	254
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	255	9	264

Error

Counts

264 → 9

Alt Table

Status	Error	Program
	34.1b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	13.8b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 (.f64 (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))) (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))))
	37.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))))
	46.3b	(/.f64 z b)
	41.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	27.7b	(+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (.f64 y z) (.f64 (+.f64 1 a) t)))
▶	13.3b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
	14.2b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	13.8b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 14477 to 6280 computations (56.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.9b	(.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	3.7b	(/.f64 y (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
	6.2b	(/.f64 (*.f64 y b) t)
✓	7.4b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))

series489.0ms (5%)

Counts

2 → 132

Calls

2 calls:

358.0ms	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
130.0ms	(.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
21×	`associate-r_binary64`
19×	`add-sqr-sqrt_binary64`
17×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 56

Calls

2 calls:

10.0ms	(.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
0.0ms	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))

simplify215.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

769×	`times-frac_binary64`
537×	`associate-/l*_binary64`
412×	`associate-/r*_binary64`
258×	`fma-def_binary64`
153×	`+-commutative_binary64`

Counts

188 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	443	12411
1	1464	11691
2	5000	11691
3	5032	11691

prune339.0ms (3.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	283	9	292

Error

Counts

292 → 9

Alt Table

Status	Error	Program
	34.1b	(.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (*.f64 (-.f64 a 1) t))
	13.8b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 (.f64 (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))) (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))))
	37.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))))
	46.3b	(/.f64 z b)
	41.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	27.7b	(+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (.f64 y z) (.f64 (+.f64 1 a) t)))
✓	13.3b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
	14.2b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
▶	13.8b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

Compiler

Compiled 15941 to 7034 computations (55.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))
✓	6.1b	(.f64 (.f64 y z) (/.f64 1 t))
	6.2b	(/.f64 (*.f64 y b) t)
✓	9.7b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

series241.0ms (2.5%)

Counts

2 → 108

Calls

2 calls:

229.0ms	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
12.0ms	(.f64 (.f64 y z) (/.f64 1 t))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
26×	`add-exp-log_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`

Counts

2 → 83

Calls

2 calls:

8.0ms	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
6.0ms	(.f64 (.f64 y z) (/.f64 1 t))

simplify136.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
604×	`associate-/l*_binary64`
431×	`associate-/r*_binary64`
274×	`fma-def_binary64`
149×	`+-commutative_binary64`

Counts

191 → 182

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	9573
1	1578	8726
2	5228	8726

prune288.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	246	9	255

Error

Counts

255 → 9

Alt Table

Status	Error	Program
✓	13.8b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	34.3b	(.f64 (/.f64 (fma.f64 y (/.f64 z t) x) (fma.f64 (.f64 y b) (-.f64 a 1) (.f64 t (fma.f64 a a -1)))) (.f64 (-.f64 a 1) t))
	37.7b	(.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))) (sqrt.f64 (/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))))
	46.3b	(/.f64 z b)
	41.3b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	27.7b	(+.f64 (/.f64 x (+.f64 1 a)) (/.f64 (.f64 y z) (.f64 (+.f64 1 a) t)))
✓	13.3b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 x (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))))
	13.8b	(fma.f64 (/.f64 y (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 z t) (.f64 (.f64 (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))))) (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))) (cbrt.f64 (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))))
	14.2b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))

Compiler

Compiled 11337 to 5320 computations (53.1% saved)

regimes3.1s (32.3%)

Accuracy

Total 4.4b remaining (81.6%)

Threshold costs 0b (0%)

Counts

139 → 6

Compiler

Compiled 33004 to 20889 computations (36.7% saved)

bsearch10.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	302
1	79	302
2	78	302

end2.0ms (0%)

Compiler: Compiled 210 to 92 computations (56.2% saved)

sample1.1s (11.6%)

Algorithm

1×

intervals

Results

545.0ms	8000×	body	128	valid
25.0ms	274×	body	128	invalid

Compiler

Compiled 503 to 269 computations (46.5% saved)

Details

analyze1.6s (16.6%)

sample61.0ms (0.6%)

simplify8.0ms (0.1%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series342.0ms (3.5%)

rewrite31.0ms (0.3%)

simplify155.0ms (1.6%)

prune273.0ms (2.8%)

localize12.0ms (0.1%)

series554.0ms (5.7%)

rewrite20.0ms (0.2%)

simplify221.0ms (2.3%)

prune354.0ms (3.6%)

localize13.0ms (0.1%)

series489.0ms (5%)

rewrite16.0ms (0.2%)

simplify215.0ms (2.2%)

prune339.0ms (3.5%)

localize12.0ms (0.1%)

series241.0ms (2.5%)

rewrite24.0ms (0.2%)

simplify136.0ms (1.4%)

prune288.0ms (3%)

regimes3.1s (32.3%)

bsearch10.0ms (0.1%)

simplify7.0ms (0.1%)

end2.0ms (0%)

sample1.1s (11.6%)

Profiling