Details

analyze1.7s (22.9%)

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)

sample69.0ms (0.9%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify10.0ms (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

11.6b

Counts

3 → 2

Alt Table

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

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	3.5b	(/.f64 (*.f64 y z) t)
✓	5.6b	(/.f64 (*.f64 y b) t)
✓	11.1b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series309.0ms (4.1%)

Counts

4 → 120

Calls

4 calls:

268.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
15.0ms	(/.f64 (*.f64 y z) t)
12.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
12.0ms	(/.f64 (*.f64 y b) t)

rewrite29.0ms (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:

12.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
4.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
3.0ms	(/.f64 (*.f64 y z) t)
3.0ms	(/.f64 (*.f64 y b) t)

simplify149.0ms (2%)

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

prune263.0ms (3.5%)

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

0.0b

Counts

203 → 10

Alt Table

Status	Error	Program
	44.5b	(-.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)))))
	14.9b	(/.f64 (+.f64 x (.f64 (.f64 y z) (/.f64 1 t))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	15.6b	(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)))))
	14.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	15.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	14.9b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	44.8b	(-.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)))))
	43.5b	(/.f64 z b)
▶	12.6b	(+.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)))))
	36.3b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t)))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2)) (/.f64 (.f64 a x) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2))))

Compiler

Compiled 10261 to 4417 computations (57% saved)

localize17.0ms (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))))
✓	4.1b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	5.6b	(/.f64 (*.f64 y b) t)
✓	9.4b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series287.0ms (3.8%)

Counts

3 → 152

Calls

3 calls:

135.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
130.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
22.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite34.0ms (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))
7.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
7.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))

simplify154.0ms (2%)

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

prune294.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	241	2	243
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	243	10	253

Error

0.0b

Counts

253 → 10

Alt Table

Status	Error	Program
	44.8b	(-.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)))))
	28.9b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
▶	12.9b	(+.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)))))
	14.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	15.6b	(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)))))
	15.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	14.9b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	44.5b	(-.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)))))
✓	12.6b	(+.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)))))
	36.3b	(-.f64 (fma.f64 (/.f64 y t) (/.f64 z (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t)))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y z) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2)) (/.f64 (.f64 a x) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2))))

Compiler

Compiled 11165 to 4423 computations (60.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.1b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	4.4b	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)
	5.6b	(/.f64 (*.f64 y b) t)
✓	7.1b	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))

series213.0ms (2.8%)

Counts

2 → 116

Calls

2 calls:

164.0ms	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))
48.0ms	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)

rewrite24.0ms (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:

9.0ms	(/.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))

simplify149.0ms (2%)

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

prune299.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	269	9	278

Error

0.0b

Counts

278 → 9

Alt Table

Status	Error	Program
	44.8b	(-.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)))))
	28.9b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	15.6b	(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)))))
	14.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	15.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
▶	12.0b	(+.f64 (.f64 (/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) z) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	14.9b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	44.5b	(-.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)))))
✓	12.6b	(+.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 10916 to 4213 computations (61.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.1b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
✓	4.9b	(.f64 (/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)) z)
	5.6b	(/.f64 (*.f64 y b) t)
✓	8.5b	(/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t))

series286.0ms (3.8%)

Counts

2 → 108

Calls

2 calls:

145.0ms	(/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t))
141.0ms	(.f64 (/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)) z)

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`associate-l_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

9.0ms	(.f64 (/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t)) z)
7.0ms	(/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t))

simplify163.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

683×	`times-frac_binary64`
492×	`associate-/l*_binary64`
436×	`associate-/r*_binary64`
233×	`associate-l_binary64`
227×	`associate-r_binary64`

Counts

164 → 157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	351	8820
1	1172	8078
2	4969	8078
3	4988	8078

prune292.0ms (3.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	255	9	264

Error

0.0b

Counts

264 → 9

Alt Table

Status	Error	Program
	44.8b	(-.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)))))
	28.9b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	15.6b	(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)))))
	14.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	15.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
✓	12.0b	(+.f64 (.f64 (/.f64 y (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) z) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))))
	14.9b	(/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 y (/.f64 t b))))
	44.5b	(-.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)))))
✓	12.6b	(+.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 11083 to 4494 computations (59.5% saved)

regimes1.5s (20.3%)

Accuracy

Total 5.0b remaining (97.2%)

Threshold costs 0b (0%)

Counts

95 → 4

Compiler

Compiled 24942 to 14506 computations (41.8% saved)

bsearch5.0ms (0.1%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	210
1	66	210
2	65	210

end1.0ms (0%)

Compiler: Compiled 148 to 63 computations (57.4% saved)

sample1.2s (15.7%)

Algorithm

1×

intervals

Results

608.0ms	8000×	body	128	valid
18.0ms	277×	body	128	invalid

Compiler

Compiled 442 to 238 computations (46.2% saved)

Details

analyze1.7s (22.9%)

sample69.0ms (0.9%)

simplify10.0ms (0.1%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series309.0ms (4.1%)

rewrite29.0ms (0.4%)

simplify149.0ms (2%)

prune263.0ms (3.5%)

localize17.0ms (0.2%)

series287.0ms (3.8%)

rewrite34.0ms (0.4%)

simplify154.0ms (2%)

prune294.0ms (3.9%)

localize16.0ms (0.2%)

series213.0ms (2.8%)

rewrite24.0ms (0.3%)

simplify149.0ms (2%)

prune299.0ms (3.9%)

localize15.0ms (0.2%)

series286.0ms (3.8%)

rewrite22.0ms (0.3%)

simplify163.0ms (2.2%)

prune292.0ms (3.8%)

regimes1.5s (20.3%)

bsearch5.0ms (0.1%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.2s (15.7%)

Profiling