Details

analyze101.0ms (1.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.3s (19.4%)

Results

676.0ms	6497×	body	128	valid
207.0ms	608×	body	1024	valid
156.0ms	680×	body	512	valid
105.0ms	467×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify198.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune3.0ms (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

13.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	21.4b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series20.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
7.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune91.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

0.1b

Counts

104 → 3

Alt Table

Status	Error	Program
	33.0b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
▶	14.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
✓	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 1942 to 1334 computations (31.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
✓	0.3b	(cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series324.0ms (4.9%)

Counts

3 → 72

Calls

3 calls:

247.0ms

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

66.0ms

(cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))

10.0ms

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

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

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

4.0ms

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

1.0ms

(cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))

simplify342.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

367×	`+-commutative_binary64`
361×	`*-commutative_binary64`
331×	`fma-def_binary64`
305×	`associate-+r+_binary64`
203×	`associate-*r/_binary64`

Counts

165 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1146	19795
1	4169	18619
2	4975	18619
3	4954	18619

prune910.0ms (13.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	397	2	399
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	398	4	402

Error

0.0b

Counts

402 → 4

Alt Table

Status	Error	Program
	33.0b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	38.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))) (pow.f64 (-.f64 1 (/.f64 y (+.f64 1 y))) 1/3))
▶	27.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))

Compiler

Compiled 45369 to 32657 computations (28% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))
✓	0.1b	(cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))
	0.3b	(cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))
	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series90.0ms (1.4%)

Counts

2 → 40

Calls

2 calls:

60.0ms

(cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

29.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
9×	`associate-r_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 53

Calls

2 calls:

6.0ms

(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))

1.0ms

(cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

624×	`fma-def_binary64`
451×	`associate-/r*_binary64`
336×	`times-frac_binary64`
231×	`associate-*r/_binary64`
218×	`associate-*l/_binary64`

Counts

93 → 125

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	7812
1	1750	7304
2	4985	7304

prune899.0ms (13.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	413	0	413
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	413	4	417

Error

0.0b

Counts

417 → 4

Alt Table

Status	Error	Program
▶	33.0b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	38.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))) (pow.f64 (-.f64 1 (/.f64 y (+.f64 1 y))) 1/3))
✓	27.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))

Compiler

Compiled 43954 to 31115 computations (29.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.4b	(/.f64 x (pow.f64 y 3))
✓	6.4b	(/.f64 x (*.f64 y y))
✓	6.7b	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
✓	9.7b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))

series163.0ms (2.5%)

Counts

4 → 72

Calls

4 calls:

93.0ms	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
24.0ms	(/.f64 x (pow.f64 y 3))
24.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
21.0ms	(/.f64 x (*.f64 y y))

rewrite160.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

270×	`*-un-lft-identity_binary64`
152×	`distribute-lft-out_binary64`
55×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
49×	`div-inv_binary64`

Counts

4 → 242

Calls

4 calls:

100.0ms	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
14.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
5.0ms	(/.f64 x (pow.f64 y 3))
3.0ms	(/.f64 x (*.f64 y y))

simplify315.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

478×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
225×	`fma-def_binary64`
208×	`associate-/r*_binary64`
151×	`times-frac_binary64`

Counts

314 → 254

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	393	18146
1	1256	12743
2	4821	12743
3	5006	12743

prune319.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	251	3	254
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	252	6	258

Error

0.0b

Counts

258 → 6

Alt Table

Status	Error	Program
	44.1b	(/.f64 (-.f64 (.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3)))) (.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))) (+.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))))
✓	13.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	49.0b	(exp.f64 (log.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (-.f64 (/.f64 (-.f64 1 x) (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))))
	33.0b	(+.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (neg.f64 (/.f64 (+.f64 (/.f64 x (.f64 y y)) (+.f64 (/.f64 1 y) (+.f64 x -1))) y)))
	38.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))) (pow.f64 (-.f64 1 (/.f64 y (+.f64 1 y))) 1/3))
✓	27.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (*.f64 (cbrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))) (cbrt.f64 (sqrt.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1))))

Compiler

Compiled 15787 to 8103 computations (48.7% saved)

regimes865.0ms (13.2%)

Accuracy

Total 0.0b remaining (15%)

Threshold costs 0.0b (15%)

Counts

81 → 3

Compiler

Compiled 12214 to 8467 computations (30.7% saved)

bsearch35.0ms (0.5%)

Steps

Iters	Range		Point
7	1411.7387488056177	120920.2554341663	12997.544702284325
10	-74591599794374.34	-1.140383595789135	-12134.734181339038

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary64`
13×	`sub-neg_binary64`
11×	`*-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	109
1	56	109
2	74	109
3	101	109
4	120	109
5	130	109
6	135	109
7	137	109
8	138	109
9	135	109

end176.0ms (2.7%)

Compiler: Compiled 410 to 257 computations (37.3% saved)

Iter	Nodes	Cost
0	36	109
1	56	109
2	74	109
3	101	109
4	120	109
5	130	109
6	135	109
7	137	109
8	138	109
9	135	109

Iter	Nodes	Cost
0	36	109
1	56	109
2	74	109
3	101	109
4	120	109
5	130	109
6	135	109
7	137	109
8	138	109
9	135	109

Details

analyze101.0ms (1.5%)

sample1.3s (19.4%)

simplify198.0ms (3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series20.0ms (0.3%)

rewrite11.0ms (0.2%)

simplify79.0ms (1.2%)

prune91.0ms (1.4%)

localize9.0ms (0.1%)

series324.0ms (4.9%)

rewrite19.0ms (0.3%)

simplify342.0ms (5.2%)

prune910.0ms (13.8%)

localize15.0ms (0.2%)

series90.0ms (1.4%)

rewrite11.0ms (0.2%)

simplify114.0ms (1.7%)

prune899.0ms (13.7%)

localize16.0ms (0.2%)

series163.0ms (2.5%)

rewrite160.0ms (2.4%)

simplify315.0ms (4.8%)

prune319.0ms (4.9%)

regimes865.0ms (13.2%)

bsearch35.0ms (0.5%)

simplify6.0ms (0.1%)

end176.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	36	109
1	56	109
2	74	109
3	101	109
4	120	109
5	130	109
6	135	109
7	137	109
8	138	109
9	135	109