Details

analyze1.1s (15.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.2s (17.8%)

Results

1.1s	8256×	body	128	valid
48.0ms	323×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

6.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.9b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series197.0ms (2.9%)

Counts

4 → 153

Calls

4 calls:

83.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
52.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
52.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
9.0ms	(-.f64 (*.f64 t z) x)

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

11.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
10.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify138.0ms (2%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
218×	`fma-def_binary64`

Counts

268 → 293

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	10265
1	1359	9717
2	5098	9717

prune302.0ms (4.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	289	5	294

Error

0.0b

Counts

294 → 5

Alt Table

Status	Error	Program
	32.1b	(/.f64 (+.f64 x (-.f64 (fma.f64 (/.f64 y (.f64 t t)) (/.f64 x z) (/.f64 y t)) (/.f64 x (.f64 t z)))) (+.f64 x 1))
	6.9b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
▶	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.4b	(/.f64 (+.f64 x (.f64 (/.f64 (-.f64 (.f64 z y) x) (.f64 (fma.f64 t z x) (-.f64 (.f64 t z) x))) (+.f64 (*.f64 t z) x))) (+.f64 x 1))
	25.8b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

Compiler

Compiled 10684 to 3956 computations (63% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	2.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	7.4b	(/.f64 z (-.f64 (*.f64 t z) x))

series144.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

82.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
23.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
22.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
17.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`
55×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

4 → 151

Calls

4 calls:

12.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
0.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify206.0ms (3%)

Algorithm

1×	egg-herbie

Rules

406×	`times-frac_binary64`
395×	`fma-neg_binary64`
363×	`associate-/l*_binary64`
249×	`associate-/r*_binary64`
140×	`associate-r_binary64`

Counts

307 → 332

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	493	12597
1	1439	9669
2	4731	9654
3	5085	9654

prune331.0ms (4.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	330	2	332
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	331	6	337

Error

Counts

337 → 6

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.4b	(/.f64 (+.f64 x (.f64 (/.f64 (-.f64 (.f64 z y) x) (.f64 (fma.f64 t z x) (-.f64 (.f64 t z) x))) (+.f64 (*.f64 t z) x))) (+.f64 x 1))
	6.9b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	23.5b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	25.8b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

Compiler

Compiled 15201 to 5058 computations (66.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	0.7b	(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))
	2.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	7.3b	(/.f64 (-.f64 (*.f64 t z) x) z)

series123.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

88.0ms

(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

26.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))

9.0ms

(/.f64 (-.f64 (*.f64 t z) x) z)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

3 → 120

Calls

3 calls:

6.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))

5.0ms

(/.f64 (-.f64 (*.f64 t z) x) z)

0.0ms

(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

simplify176.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

370×	`times-frac_binary64`
297×	`sub-neg_binary64`
279×	`associate-/l*_binary64`
261×	`fma-neg_binary64`
250×	`associate-/r*_binary64`

Counts

240 → 254

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	326	7319
1	951	6735
2	4112	6501
3	4862	6500
4	4966	6500

prune368.0ms (5.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	325	6	331

Error

Counts

331 → 6

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.4b	(/.f64 (+.f64 x (.f64 (/.f64 (-.f64 (.f64 z y) x) (.f64 (fma.f64 t z x) (-.f64 (.f64 t z) x))) (+.f64 (*.f64 t z) x))) (+.f64 x 1))
	6.9b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	0.1b	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
	25.8b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

Compiler

Compiled 13214 to 5107 computations (61.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
✓	0.1b	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
✓	2.2b	(/.f64 x (-.f64 (*.f64 z t) x))
✓	4.9b	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))

series375.0ms (5.5%)

Counts

4 → 168

Calls

4 calls:

190.0ms	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
149.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
20.0ms	(/.f64 x (-.f64 (*.f64 z t) x))
16.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))

rewrite83.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-sqr-sqrt_binary64`
135×	`*-un-lft-identity_binary64`
113×	`times-frac_binary64`
109×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`

Counts

4 → 248

Calls

4 calls:

27.0ms	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
13.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
9.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
4.0ms	(/.f64 x (-.f64 (*.f64 z t) x))

simplify312.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
420×	`distribute-rgt-in_binary64`
310×	`distribute-lft-in_binary64`
258×	`neg-sub0_binary64`
254×	`neg-mul-1_binary64`

Counts

416 → 451

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	844	18686
1	2673	16275
2	4555	16247
3	4963	16247

prune543.0ms (7.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	451	0	451
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	451	6	457

Error

Counts

457 → 6

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.4b	(/.f64 (+.f64 x (.f64 (/.f64 (-.f64 (.f64 z y) x) (.f64 (fma.f64 t z x) (-.f64 (.f64 t z) x))) (+.f64 (*.f64 t z) x))) (+.f64 x 1))
	6.9b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	0.1b	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
	25.8b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 1 (pow.f64 x 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))))

Compiler

Compiled 22929 to 9352 computations (59.2% saved)

regimes932.0ms (13.6%)

Accuracy

Total 0.0b remaining (76.6%)

Threshold costs 0.0b (76.6%)

Counts

147 → 1

Compiler

Compiled 18498 to 11526 computations (37.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
1	28	37
2	40	37
3	46	37
4	49	37
5	48	37

end105.0ms (1.5%)

Compiler: Compiled 239 to 144 computations (39.7% saved)

Details

analyze1.1s (15.7%)

sample1.2s (17.8%)

simplify93.0ms (1.4%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series197.0ms (2.9%)

rewrite37.0ms (0.5%)

simplify138.0ms (2%)

prune302.0ms (4.4%)

localize12.0ms (0.2%)

series144.0ms (2.1%)

rewrite32.0ms (0.5%)

simplify206.0ms (3%)

prune331.0ms (4.8%)

localize13.0ms (0.2%)

series123.0ms (1.8%)

rewrite19.0ms (0.3%)

simplify176.0ms (2.6%)

prune368.0ms (5.3%)

localize15.0ms (0.2%)

series375.0ms (5.5%)

rewrite83.0ms (1.2%)

simplify312.0ms (4.5%)

prune543.0ms (7.9%)

regimes932.0ms (13.6%)

simplify4.0ms (0.1%)

end105.0ms (1.5%)

Profiling