Details

analyze1.7s (21.8%)

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 (0.8%)

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 (0.1%)

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

12.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
▶	16.2b	(/.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)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (fma.f64 b (/.f64 y t) a))
✓	2.2b	(fma.f64 b (/.f64 y t) a)
✓	2.8b	(fma.f64 y (/.f64 z t) x)
✓	12.0b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))

series256.0ms (3.3%)

Counts

4 → 216

Calls

4 calls:

210.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
17.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
15.0ms	(fma.f64 y (/.f64 z t) x)
13.0ms	(fma.f64 b (/.f64 y t) a)

rewrite13.0ms (0.2%)

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:

6.0ms	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
3.0ms	(+.f64 1 (fma.f64 b (/.f64 y t) a))
0.0ms	(fma.f64 b (/.f64 y t) a)
0.0ms	(fma.f64 y (/.f64 z t) x)

simplify142.0ms (1.9%)

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

prune195.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	150	8	158
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	151	9	160

Error

0.2b

Counts

160 → 9

Alt Table

Status	Error	Program
	16.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 (fma.f64 b (/.f64 y t) 1) a))
▶	14.9b	(+.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)))))
	17.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	15.0b	(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))))
	43.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (log.f64 (exp.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	43.7b	(-.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)))))
	44.1b	(/.f64 z b)
	17.0b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 y (/.f64 z t) x)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))) (/.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)) (cbrt.f64 (fma.f64 y (/.f64 z t) x))))
	16.3b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 8582 to 3875 computations (54.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	4.3b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	5.6b	(/.f64 (*.f64 y b) t)
✓	11.7b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series292.0ms (3.8%)

Counts

4 → 152

Calls

4 calls:

132.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
121.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
23.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
15.0ms	(/.f64 (*.f64 y b) t)

rewrite35.0ms (0.5%)

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))
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)
3.0ms	(/.f64 (*.f64 y b) t)

simplify190.0ms (2.5%)

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

prune310.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	267	2	269
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	269	9	278

Error

0.2b

Counts

278 → 9

Alt Table

Status	Error	Program
	16.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 (fma.f64 b (/.f64 y t) 1) a))
✓	14.9b	(+.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)))))
▶	13.6b	(+.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)))))
	27.5b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	43.7b	(-.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)))))
	17.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	15.0b	(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))))
	43.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (log.f64 (exp.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	16.3b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 11810 to 4510 computations (61.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.3b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	4.8b	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)
	5.6b	(/.f64 (*.f64 y b) t)
✓	7.5b	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))

series170.0ms (2.2%)

Counts

2 → 116

Calls

2 calls:

126.0ms	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))
44.0ms	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 75

Calls

2 calls:

11.0ms	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)
9.0ms	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))

simplify148.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

522×	`times-frac_binary64`
404×	`associate-/l*_binary64`
275×	`associate-/r*_binary64`
198×	`fma-neg_binary64`
179×	`associate-r_binary64`

Counts

191 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	7427
1	945	6768
2	4538	6692
3	5064	6692

prune280.0ms (3.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	272	0	272
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	272	9	281

Error

0.2b

Counts

281 → 9

Alt Table

Status	Error	Program
	16.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 (fma.f64 b (/.f64 y t) 1) a))
✓	14.9b	(+.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)))))
✓	13.6b	(+.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)))))
	27.5b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	43.7b	(-.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)))))
	17.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
▶	15.0b	(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))))
	43.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (log.f64 (exp.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	16.3b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 10940 to 4180 computations (61.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.2b	(fma.f64 b (/.f64 y t) a)
✓	3.1b	(/.f64 x (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	5.4b	(/.f64 y (+.f64 1 (fma.f64 b (/.f64 y t) a)))
✓	8.6b	(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))))

series495.0ms (6.5%)

Counts

3 → 180

Calls

3 calls:

299.0ms

(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))))

116.0ms

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

79.0ms

(/.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:

4.0ms

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

4.0ms

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

1.0ms

(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))))

simplify214.0ms (2.8%)

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

prune276.0ms (3.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	234	9	243

Error

Counts

243 → 9

Alt Table

Status	Error	Program
	16.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 (fma.f64 b (/.f64 y t) 1) a))
✓	14.9b	(+.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)))))
✓	13.6b	(+.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)))))
	39.1b	(/.f64 (+.f64 (/.f64 (*.f64 t x) y) z) b)
	17.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
✓	15.0b	(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))))
	43.2b	(/.f64 (fma.f64 y (/.f64 z t) x) (log.f64 (exp.f64 (+.f64 1 (fma.f64 b (/.f64 y t) a)))))
	43.7b	(-.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)))))
	16.3b	(*.f64 (fma.f64 y (/.f64 z t) x) (/.f64 1 (+.f64 1 (fma.f64 b (/.f64 y t) a))))

Compiler

Compiled 13140 to 5870 computations (55.3% saved)

regimes1.7s (22.3%)

Accuracy

Total 5.4b remaining (98.6%)

Threshold costs 0b (0%)

Counts

87 → 4

Compiler

Compiled 19327 to 11549 computations (40.2% saved)

bsearch4.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	193
1	48	193
2	47	193

end1.0ms (0%)

Compiler: Compiled 138 to 51 computations (63% saved)

sample1.1s (14.2%)

Algorithm

1×

intervals

Results

532.0ms	8000×	body	128	valid
18.0ms	298×	body	128	invalid

Compiler

Compiled 406 to 211 computations (48% saved)

Details

analyze1.7s (21.8%)

sample61.0ms (0.8%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series256.0ms (3.3%)

rewrite13.0ms (0.2%)

simplify142.0ms (1.9%)

prune195.0ms (2.5%)

localize12.0ms (0.2%)

series292.0ms (3.8%)

rewrite35.0ms (0.5%)

simplify190.0ms (2.5%)

prune310.0ms (4.1%)

localize13.0ms (0.2%)

series170.0ms (2.2%)

rewrite26.0ms (0.3%)

simplify148.0ms (1.9%)

prune280.0ms (3.7%)

localize11.0ms (0.1%)

series495.0ms (6.5%)

rewrite13.0ms (0.2%)

simplify214.0ms (2.8%)

prune276.0ms (3.6%)

regimes1.7s (22.3%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (14.2%)

Profiling