Details

analyze1.8s (19%)

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	7×	body	128	invalid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify11.0ms (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

12.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
▶	16.5b	(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y z) t))
✓	4.5b	(/.f64 (*.f64 y z) t)
✓	5.6b	(/.f64 (*.f64 y b) t)
✓	12.5b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))

series262.0ms (2.8%)

Counts

4 → 120

Calls

4 calls:

226.0ms	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
13.0ms	(/.f64 (*.f64 y z) t)
11.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
11.0ms	(/.f64 (*.f64 y b) t)

rewrite41.0ms (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)))
3.0ms	(+.f64 x (/.f64 (*.f64 y z) t))
3.0ms	(/.f64 (*.f64 y b) t)
3.0ms	(/.f64 (*.f64 y z) t)

simplify178.0ms (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

prune242.0ms (2.6%)

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

0.1b

Counts

203 → 10

Alt Table

Status	Error	Program
▶	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 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	16.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 t (.f64 y z)))) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	16.8b	(/.f64 1 (/.f64 (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)) (+.f64 x (/.f64 (.f64 y z) t))))
	16.7b	(/.f64 (+.f64 x (/.f64 (.f64 y z) t)) (+.f64 (+.f64 a 1) (.f64 (/.f64 y (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))
	40.3b	(-.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)))))
	41.3b	(/.f64 z b)
	17.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	40.3b	(-.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))))
	39.6b	(-.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 10257 to 4419 computations (56.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
✓	5.2b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	5.6b	(/.f64 (*.f64 y b) t)
✓	10.8b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series265.0ms (2.8%)

Counts

3 → 152

Calls

3 calls:

132.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))
116.0ms	(/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))))
17.0ms	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)

rewrite33.0ms (0.3%)

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:

11.0ms	(/.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)

simplify136.0ms (1.4%)

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

prune322.0ms (3.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	238	5	243
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	243	10	253

Error

0.1b

Counts

253 → 10

Alt Table

Status	Error	Program
	27.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 t (.f64 y z)))) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	14.7b	(+.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)))))
	40.3b	(-.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)))))
	14.7b	(+.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)))))
	33.4b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (-.f64 (/.f64 x (+.f64 1 (/.f64 (.f64 y b) t))) (/.f64 (.f64 a x) (pow.f64 (+.f64 1 (/.f64 (.f64 y b) t)) 2))))
	17.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.4b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
▶	14.0b	(+.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 (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))))
	39.6b	(-.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 11186 to 4443 computations (60.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(/.f64 x (+.f64 1 (+.f64 a (.f64 (/.f64 y (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t))))))
	5.2b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	5.6b	(/.f64 (*.f64 y b) t)
	10.8b	(/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t))) t))

series127.0ms (1.3%)

Counts

1 → 60

Calls

1 calls:

127.0ms

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 35

Calls

1 calls:

5.0ms

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

simplify162.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
324×	`cancel-sign-sub-inv_binary64`
319×	`times-frac_binary64`
229×	`associate-/l*_binary64`
192×	`associate-/r*_binary64`

Counts

95 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	5314
1	646	4946
2	2978	4866
3	4980	4866
4	4997	4866
5	4975	4866

prune296.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	237	10	247

Error

0.1b

Counts

247 → 10

Alt Table

Status	Error	Program
	32.7b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (-.f64 (/.f64 x (fma.f64 (/.f64 y t) b 1)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 (/.f64 y t) b 1) 2))))
▶	14.7b	(+.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)))))
	27.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 t (.f64 y z)))) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	14.7b	(+.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)))))
	40.3b	(-.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)))))
	17.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.4b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
✓	14.0b	(+.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 (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))))
	39.6b	(-.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 12779 to 4448 computations (65.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.9b	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)
	5.2b	(.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)
	5.6b	(/.f64 (*.f64 y b) t)
✓	7.8b	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))

series180.0ms (1.9%)

Counts

2 → 116

Calls

2 calls:

136.0ms	(/.f64 y (/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z))
43.0ms	(/.f64 (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t) z)

rewrite22.0ms (0.2%)

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

simplify149.0ms (1.6%)

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

prune322.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	268	10	278

Error

0.1b

Counts

278 → 10

Alt Table

Status	Error	Program
	27.1b	(+.f64 (/.f64 z b) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
	16.6b	(/.f64 (+.f64 x (/.f64 1 (/.f64 t (.f64 y z)))) (+.f64 (+.f64 a 1) (/.f64 (.f64 y b) t)))
	32.7b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t))) t)) (-.f64 (/.f64 x (fma.f64 (/.f64 y t) b 1)) (/.f64 (.f64 x a) (pow.f64 (fma.f64 (/.f64 y t) b 1) 2))))
	11.0b	(+.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)))))
	17.9b	(/.f64 (fma.f64 y (/.f64 z t) x) (+.f64 1 (fma.f64 b (/.f64 y t) a)))
	18.4b	(/.f64 (+.f64 x (/.f64 y (/.f64 t z))) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))
	18.4b	(+.f64 (.f64 (/.f64 1 (+.f64 1 (+.f64 a (/.f64 (.f64 y b) t)))) (/.f64 y (/.f64 t z))) (/.f64 x (+.f64 1 (+.f64 a (/.f64 (*.f64 y b) t)))))
✓	14.0b	(+.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 (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 b (cbrt.f64 t)))))))
	39.6b	(-.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)))))
	40.3b	(-.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)))))

Compiler

Compiled 10734 to 4112 computations (61.7% saved)

regimes3.7s (38.6%)

Accuracy

Total 5.8b remaining (95.9%)

Threshold costs 0b (0%)

Counts

212 → 3

Compiler

Compiled 57440 to 34322 computations (40.2% saved)

bsearch9.0ms (0.1%)

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

simplify4.0ms (0%)

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	46	186
1	65	186
2	64	186

end3.0ms (0%)

Compiler: Compiled 129 to 56 computations (56.6% saved)

sample1.1s (11.8%)

Algorithm

1×

intervals

Results

551.0ms	8000×	body	128	valid
20.0ms	284×	body	128	invalid

Compiler

Compiled 472 to 265 computations (43.9% saved)

Details

analyze1.8s (19%)

sample61.0ms (0.6%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series262.0ms (2.8%)

rewrite41.0ms (0.4%)

simplify178.0ms (1.9%)

prune242.0ms (2.6%)

localize13.0ms (0.1%)

series265.0ms (2.8%)

rewrite33.0ms (0.3%)

simplify136.0ms (1.4%)

prune322.0ms (3.4%)

localize20.0ms (0.2%)

series127.0ms (1.3%)

rewrite8.0ms (0.1%)

simplify162.0ms (1.7%)

prune296.0ms (3.1%)

localize13.0ms (0.1%)

series180.0ms (1.9%)

rewrite22.0ms (0.2%)

simplify149.0ms (1.6%)

prune322.0ms (3.4%)

regimes3.7s (38.6%)

bsearch9.0ms (0.1%)

simplify4.0ms (0%)

end3.0ms (0%)

sample1.1s (11.8%)

Profiling