Details

analyze985.0ms (13.7%)

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)

sample90.0ms (1.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify94.0ms (1.3%)

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

5.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.5b	(/.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 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.0b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	8.0b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series215.0ms (3%)

Counts

4 → 153

Calls

4 calls:

89.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
66.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
53.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
7.0ms	(-.f64 (*.f64 t z) x)

rewrite41.0ms (0.6%)

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:

13.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
12.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify151.0ms (2.1%)

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

prune305.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	287	6	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	6	294

Error

0.0b

Counts

294 → 6

Alt Table

Status	Error	Program
	16.3b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)) 3))) (+.f64 x 1))
	5.5b	(/.f64 (+.f64 x (-.f64 (/.f64 (.f64 y z) (-.f64 (.f64 t z) x)) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	21.8b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	6.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))
▶	1.3b	(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)))
	15.3b	(/.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))

Compiler

Compiled 10712 to 3956 computations (63.1% saved)

localize14.0ms (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)))
✓	2.0b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	5.4b	(/.f64 z (-.f64 (*.f64 t z) x))

series156.0ms (2.2%)

Counts

4 → 156

Calls

4 calls:

85.0ms	(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)))
26.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
25.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
20.0ms	(/.f64 z (-.f64 (*.f64 t z) x))

rewrite34.0ms (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:

10.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
5.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
1.0ms	(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)))

simplify269.0ms (3.7%)

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

prune466.0ms (6.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	330	2	332
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	332	6	338

Error

Counts

338 → 6

Alt Table

Status	Error	Program
	16.3b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)) 3))) (+.f64 x 1))
	5.5b	(/.f64 (+.f64 x (-.f64 (/.f64 (.f64 y z) (-.f64 (.f64 t z) x)) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	2.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))
▶	1.3b	(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)))
	21.8b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	6.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 15219 to 5056 computations (66.8% saved)

localize19.0ms (0.3%)

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)))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))
	2.0b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	5.4b	(/.f64 (-.f64 (*.f64 t z) x) z)

series162.0ms (2.2%)

Counts

3 → 120

Calls

3 calls:

131.0ms

(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)))

21.0ms

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

10.0ms

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

rewrite21.0ms (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)))

simplify192.0ms (2.7%)

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

prune301.0ms (4.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	328	3	331

Error

Counts

331 → 3

Alt Table

Status	Error	Program
	2.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.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)))))
	6.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 13106 to 5033 computations (61.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 x (-.f64 (*.f64 z t) x)))
✓	0.0b	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
✓	2.0b	(/.f64 x (-.f64 (*.f64 z t) x))
✓	4.0b	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))

series206.0ms (2.9%)

Counts

4 → 156

Calls

4 calls:

150.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
22.0ms	(/.f64 x (-.f64 (*.f64 z t) x))
18.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 z t) x)))
16.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`add-sqr-sqrt_binary64`
148×	`*-un-lft-identity_binary64`
142×	`add-cube-cbrt_binary64`
123×	`prod-diff_binary64`
122×	`times-frac_binary64`

Counts

4 → 279

Calls

4 calls:

15.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
12.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
9.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 z t) x)))
5.0ms	(/.f64 x (-.f64 (*.f64 z t) x))

simplify414.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

647×	`times-frac_binary64`
397×	`distribute-rgt-in_binary64`
377×	`fma-def_binary64`
192×	`fma-neg_binary64`
190×	`*-commutative_binary64`

Counts

435 → 480

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	794	18024
1	2356	14058
2	4746	14058
3	4955	14058
4	5033	14058

prune468.0ms (6.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	480	0	480
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	480	3	483

Error

Counts

483 → 3

Alt Table

Status	Error	Program
	2.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.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)))))
	6.0b	(/.f64 (+.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (cbrt.f64 (-.f64 (.f64 z y) x))) (/.f64 (cbrt.f64 (-.f64 (.f64 z y) x)) (-.f64 (.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 23109 to 7902 computations (65.8% saved)

regimes1.3s (18.2%)

Accuracy

Total 0.0b remaining (58.3%)

Threshold costs 0.0b (58.3%)

Counts

178 → 1

Compiler

Compiled 21708 to 13679 computations (37% saved)

simplify3.0ms (0%)

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

end1.0ms (0%)

Compiler: Compiled 29 to 18 computations (37.9% saved)

sample1.2s (16.6%)

Algorithm

1×

intervals

Results

579.0ms	8000×	body	128	valid
24.0ms	326×	body	128	invalid

Compiler

Compiled 151 to 90 computations (40.4% saved)

Details

analyze985.0ms (13.7%)

sample90.0ms (1.2%)

simplify94.0ms (1.3%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series215.0ms (3%)

rewrite41.0ms (0.6%)

simplify151.0ms (2.1%)

prune305.0ms (4.2%)

localize14.0ms (0.2%)

series156.0ms (2.2%)

rewrite34.0ms (0.5%)

simplify269.0ms (3.7%)

prune466.0ms (6.5%)

localize19.0ms (0.3%)

series162.0ms (2.2%)

rewrite21.0ms (0.3%)

simplify192.0ms (2.7%)

prune301.0ms (4.2%)

localize14.0ms (0.2%)

series206.0ms (2.9%)

rewrite74.0ms (1%)

simplify414.0ms (5.7%)

prune468.0ms (6.5%)

regimes1.3s (18.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.2s (16.6%)

Profiling