Details

analyze96.0ms (2%)

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
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample898.0ms (18.7%)

Results

809.0ms	8256×	body	128	valid
15.0ms	186×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

rewrite42.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

692×	`log1p-expm1-u_binary64`
692×	`expm1-log1p-u_binary64`
132×	`prod-diff_binary64`
131×	`fma-def_binary64`
128×	`expm1-udef_binary64`

Counts

1 → 52

Calls

1 calls:

41.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	144	10
2	1759	10
3	4956	10
0	0	0
1	0	0

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

423×	`fma-neg_binary64`
367×	`neg-sub0_binary64`
365×	`distribute-rgt-neg-in_binary64`
361×	`neg-mul-1_binary64`
345×	`associate-r_binary64`

Counts

76 → 59

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	232
1	41	232
2	78	232
3	166	232
4	444	232
5	1310	232
6	2464	232
7	4517	232
8	4907	232

prune35.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	54	5	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	5	60

Error

0.0b

Counts

60 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
	32.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 x y) (-.f64 1 y)) 3))
	1.1b	(pow.f64 (cbrt.f64 (.f64 (.f64 x y) (-.f64 1 y))) 3)
	15.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 y 3)) (.f64 x y)) (+.f64 1 (fma.f64 y y y)))
	8.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 812 to 300 computations (63.1% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
✓	0.2b	(.f64 (neg.f64 y) (.f64 x y))

series19.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
9.0ms	(.f64 (neg.f64 y) (.f64 x y))

rewrite80.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

551×	`log1p-expm1-u_binary64`
551×	`expm1-log1p-u_binary64`
450×	`prod-diff_binary64`
331×	`log-prod_binary64`
231×	`egg-rr`

Counts

2 → 231

Calls

2 calls:

73.0ms	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
73.0ms	(.f64 (neg.f64 y) (.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	145	17
2	1483	17
3	5190	17
0	0	0
1	0	0

simplify162.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1315×	`difference-of-squares_binary64`
881×	`unsub-neg_binary64`
792×	`sub-neg_binary64`
531×	`fma-neg_binary64`
424×	`neg-mul-1_binary64`

Counts

279 → 238

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	15	448
1	40	448
2	82	448
3	188	448
4	510	448
5	1250	448
6	2607	448
7	4092	448
8	4521	448
9	4833	354
10	2918	354
11	3366	354
12	3484	354
13	6450	354

prune259.0ms (5.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	237	6	243

Error

0.0b

Counts

243 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
	32.0b	(cbrt.f64 (pow.f64 (.f64 (.f64 x y) (-.f64 1 y)) 3))
▶	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
	9.0b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 y x)) (cbrt.f64 (.f64 y y))))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 y) (.f64 y x))) (cbrt.f64 (.f64 y y)) (.f64 (.f64 (cbrt.f64 y) (.f64 y x)) (cbrt.f64 (*.f64 y y)))))
	15.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 y 3)) (.f64 x y)) (+.f64 1 (fma.f64 y y y)))
	8.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 7811 to 1483 computations (81% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
✓	9.4b	(cbrt.f64 (*.f64 y x))
✓	44.0b	(fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2)))

series919.0ms (19.1%)

Counts

4 → 96

Calls

4 calls:

352.0ms	(cbrt.f64 (*.f64 y x))
310.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
223.0ms	(fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2)))
33.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2))

rewrite64.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

880×	`expm1-log1p-u_binary64`
832×	`prod-diff_binary64`
114×	`associate-r_binary64`
111×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

4 → 87

Calls

4 calls:

62.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2))
62.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
62.0ms	(cbrt.f64 (*.f64 y x))
62.0ms	(fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	77
1	229	38
2	2372	38
3	5294	38
0	0	0
1	0	0

simplify127.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-neg_binary64`
488×	`unswap-sqr_binary64`
349×	`fma-def_binary64`
216×	`exp-diff_binary64`
200×	`exp-prod_binary64`

Counts

183 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	83	1920
1	208	1892
2	370	1684
3	1277	1304
4	4364	1295
5	5003	1295

prune518.0ms (10.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	351	4	355
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	352	9	361

Error

Counts

361 → 9

Alt Table

Status	Error	Program
	3.2b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 y x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y x)) 4))))))
	15.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 y 3)) (.f64 x y)) (+.f64 1 (fma.f64 y y y)))
▶	0.5b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 y x)))) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (/.f64 -1 y))) (cbrt.f64 -1)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
✓	0.1b	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
✓	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
	9.0b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 y x)) (cbrt.f64 (.f64 y y))))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 y) (.f64 y x))) (cbrt.f64 (.f64 y y)) (.f64 (.f64 (cbrt.f64 y) (.f64 y x)) (cbrt.f64 (*.f64 y y)))))
	8.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 17388 to 5596 computations (67.8% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 y)
	9.4b	(cbrt.f64 (*.f64 y x))
✓	43.5b	(fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 y x)))) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2)))

series319.0ms (6.7%)

Counts

3 → 48

Calls

3 calls:

263.0ms

(fma.f64 (neg.f64 (*.f64 (cbrt.f64 (*.f64 y x)) y)) (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 y x)))) (*.f64 (*.f64 (cbrt.f64 (*.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2)))

28.0ms

(cbrt.f64 x)

28.0ms

(cbrt.f64 y)

rewrite62.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

720×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
203×	`log-pow_binary64`
186×	`fma-def_binary64`

Counts

3 → 84

Calls

3 calls:

60.0ms

(cbrt.f64 x)

60.0ms

(cbrt.f64 y)

60.0ms

(fma.f64 (neg.f64 (*.f64 (cbrt.f64 (*.f64 y x)) y)) (*.f64 (cbrt.f64 y) (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 y x)))) (*.f64 (*.f64 (cbrt.f64 (*.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	287	22
2	3008	20
3	5183	20
0	0	0
1	0	0

simplify108.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
486×	`exp-sum_binary64`
477×	`exp-prod_binary64`
253×	`fma-neg_binary64`
240×	`exp-diff_binary64`

Counts

132 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	93	1006
1	249	880
2	465	823
3	1454	692
4	4357	662
5	4842	662
6	4171	662
7	4933	662

prune497.0ms (10.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	299	9	308

Error

Counts

308 → 9

Alt Table

Status	Error	Program
	9.0b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 y) (.f64 y x)) (cbrt.f64 (.f64 y y))))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 y) (.f64 y x))) (cbrt.f64 (.f64 y y)) (.f64 (.f64 (cbrt.f64 y) (.f64 y x)) (cbrt.f64 (*.f64 y y)))))
	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 y)) 3) (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 y x)))) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
✓	0.5b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 y x)))) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x (/.f64 -1 y))) (cbrt.f64 -1)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
✓	0.1b	(fma.f64 x y (.f64 (neg.f64 y) (.f64 x y)))
	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
✓	0.6b	(+.f64 (fma.f64 y x (neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (.f64 y x)) 2)))) (fma.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 y x)) y)) (pow.f64 (cbrt.f64 (.f64 y x)) 2) (.f64 (.f64 (cbrt.f64 (.f64 y x)) y) (pow.f64 (cbrt.f64 (*.f64 y x)) 2))))
	15.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 y 3)) (.f64 x y)) (+.f64 1 (fma.f64 y y y)))
	8.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

Compiler

Compiled 15437 to 4348 computations (71.8% saved)

regimes289.0ms (6%)

Accuracy

Total 0.1b remaining (79.7%)

Threshold costs 0.1b (79.7%)

Counts

86 → 1

Compiler

Compiled 9848 to 3613 computations (63.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	15	13
2	22	13
3	33	13
4	38	13
5	41	13
6	42	13
7	42	13

end161.0ms (3.3%)

Compiler: Compiled 353 to 157 computations (55.5% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze96.0ms (2%)

sample898.0ms (18.7%)

simplify24.0ms (0.5%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite42.0ms (0.9%)

simplify69.0ms (1.4%)

prune35.0ms (0.7%)

localize5.0ms (0.1%)

series19.0ms (0.4%)

rewrite80.0ms (1.7%)

simplify162.0ms (3.4%)

prune259.0ms (5.4%)

localize13.0ms (0.3%)

series919.0ms (19.1%)

rewrite64.0ms (1.3%)

simplify127.0ms (2.7%)

prune518.0ms (10.8%)

localize18.0ms (0.4%)

series319.0ms (6.7%)

rewrite62.0ms (1.3%)

simplify108.0ms (2.2%)

prune497.0ms (10.4%)

regimes289.0ms (6%)

simplify3.0ms (0.1%)

end161.0ms (3.3%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10