Details

analyze743.0ms (8.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	62.5%	0%	5
43.7%	56.2%	0%	6
46.9%	53.1%	0%	7
46.9%	53.1%	0%	8
46.9%	53.1%	0%	9
47%	52.9%	0%	10
47.1%	52.8%	0%	11
47.2%	52.8%	0%	12
47.3%	52.7%	0%	13
47.3%	52.6%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.7s (19.1%)

Results

681.0ms	2110×	body	1024	valid
450.0ms	4417×	body	128	valid
249.0ms	975×	body	512	valid
98.0ms	527×	body	256	valid
90.0ms	227×	body	2048	valid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	3.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

rewrite221.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1304×	`*-un-lft-identity_binary64`
1000×	`times-frac_binary64`
859×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
523×	`add-cube-cbrt_binary64`

Counts

2 → 748

Calls

2 calls:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify784.0ms (9%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-neg_binary64`
418×	`distribute-rgt-in_binary64`
361×	`unsub-neg_binary64`
255×	`fma-udef_binary64`
202×	`associate-+r-_binary64`

Counts

772 → 551

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	521	54026
1	1234	30580
2	2848	22272
3	4495	22270
4	4718	22270

prune762.0ms (8.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	547	4	551
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	547	5	552

Error

0.0b

Counts

552 → 5

Alt Table

Status	Error	Program
	31.1b	(+.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))
▶	31.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	31.1b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
	32.5b	(fma.f64 3 x 1)
✓	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 29250 to 21634 computations (26% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	0.3b	(/.f64 3 (pow.f64 x 3))
✓	0.3b	(/.f64 1 (*.f64 x x))
✓	8.3b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

series12.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
3.0ms	(/.f64 3 (pow.f64 x 3))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite80.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

178×	`*-un-lft-identity_binary64`
136×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
96×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`

Counts

4 → 245

Calls

4 calls:

27.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
21.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
4.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 1 (*.f64 x x))

simplify193.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

508×	`unswap-sqr_binary64`
388×	`cancel-sign-sub-inv_binary64`
372×	`fma-neg_binary64`
185×	`associate-l_binary64`
185×	`associate-/r*_binary64`

Counts

281 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	8270
1	610	6566
2	2500	5026
3	4684	5026
4	4880	5026

prune228.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	273	6	279

Error

0.0b

Counts

279 → 6

Alt Table

Status	Error	Program
▶	31.1b	(+.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))
✓	31.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	31.1b	(fma.f64 -3 (/.f64 1 x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
	32.5b	(fma.f64 3 x 1)
	45.9b	(fma.f64 (sqrt.f64 (/.f64 -3 x)) (sqrt.f64 (/.f64 -3 x)) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
✓	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 9591 to 6666 computations (30.5% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
✓	2.9b	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	4.4b	(/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3)))
✓	30.8b	(fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))

series137.0ms (1.6%)

Counts

4 → 48

Calls

4 calls:

110.0ms	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
11.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
10.0ms	(fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))
6.0ms	(/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3)))

rewrite96.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

373×	`*-un-lft-identity_binary64`
224×	`cbrt-prod_binary64`
224×	`times-frac_binary64`
211×	`add-sqr-sqrt_binary64`
83×	`add-cube-cbrt_binary64`

Counts

4 → 260

Calls

4 calls:

35.0ms	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))
13.0ms	(/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3)))
0.0ms	(fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))
0.0ms	(fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))

simplify523.0ms (6%)

Algorithm

1×	egg-herbie

Rules

601×	`times-frac_binary64`
258×	`fma-neg_binary64`
203×	`fma-def_binary64`
188×	`associate-r_binary64`
180×	`associate-l_binary64`

Counts

308 → 350

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	397	9504
1	869	9036
2	2814	8552
3	4612	8468
4	4984	8468
5	4847	8468

prune2.0s (22.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	741	1	742
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	742	6	748

Error

Counts

748 → 6

Alt Table

Status	Error	Program
	31.9b	(+.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))
✓	31.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
▶	31.1b	(fma.f64 -3 (/.f64 1 x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
	32.5b	(fma.f64 3 x 1)
	45.9b	(fma.f64 (sqrt.f64 (/.f64 -3 x)) (sqrt.f64 (/.f64 -3 x)) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
✓	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 82690 to 63625 computations (23.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 -3 (/.f64 1 x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
✓	0.3b	(/.f64 -3 (pow.f64 x 3))
	0.3b	(/.f64 1 (*.f64 x x))
✓	6.6b	(-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))

series12.0ms (0.1%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(fma.f64 -3 (/.f64 1 x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
4.0ms	(-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))
3.0ms	(/.f64 -3 (pow.f64 x 3))

rewrite91.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

471×	`times-frac_binary64`
320×	`add-sqr-sqrt_binary64`
296×	`*-un-lft-identity_binary64`
286×	`add-cube-cbrt_binary64`
280×	`prod-diff_binary64`

Counts

3 → 436

Calls

3 calls:

25.0ms	(-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))
5.0ms	(/.f64 -3 (pow.f64 x 3))
0.0ms	(fma.f64 -3 (/.f64 1 x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))

simplify408.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
399×	`associate-/l/_binary64`
369×	`fma-neg_binary64`
275×	`cancel-sign-sub-inv_binary64`
233×	`log-div_binary64`

Counts

460 → 397

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	299	13821
1	479	11693
2	1543	8705
3	4405	8377
4	4792	8377
5	4988	8377
6	4861	8377

prune381.0ms (4.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	434	0	434
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	434	6	440

Error

Counts

440 → 6

Alt Table

Status	Error	Program
	31.9b	(+.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (.f64 (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (cbrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))))
✓	31.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	31.1b	(fma.f64 -3 (/.f64 1 x) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
	32.5b	(fma.f64 3 x 1)
	45.9b	(fma.f64 (sqrt.f64 (/.f64 -3 x)) (sqrt.f64 (/.f64 -3 x)) (-.f64 (/.f64 -3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
✓	30.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 16469 to 11874 computations (27.9% saved)

regimes116.0ms (1.3%)

Accuracy

Total 0.2b remaining (81.3%)

Threshold costs 0.2b (81.3%)

Counts

35 → 2

Compiler

Compiled 2282 to 1744 computations (23.6% saved)

bsearch2.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	62
1	34	62
2	47	62
3	64	62
4	75	62
5	80	62
6	81	62
7	77	62

end153.0ms (1.7%)

Compiler: Compiled 264 to 201 computations (23.9% saved)

Details

analyze743.0ms (8.5%)

sample1.7s (19.1%)

simplify88.0ms (1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite221.0ms (2.5%)

simplify784.0ms (9%)

prune762.0ms (8.7%)

localize13.0ms (0.1%)

series12.0ms (0.1%)

rewrite80.0ms (0.9%)

simplify193.0ms (2.2%)

prune228.0ms (2.6%)

localize23.0ms (0.3%)

series137.0ms (1.6%)

rewrite96.0ms (1.1%)

simplify523.0ms (6%)

prune2.0s (22.6%)

localize10.0ms (0.1%)

series12.0ms (0.1%)

rewrite91.0ms (1%)

simplify408.0ms (4.7%)

prune381.0ms (4.4%)

regimes116.0ms (1.3%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end153.0ms (1.7%)

Profiling