Details

analyze35.0ms (1.6%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample789.0ms (36.4%)

Results

695.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify70.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

prune1.0ms (0.1%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 47

Calls

1 calls:

6.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

simplify92.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
387×	`distribute-rgt-in_binary64`
223×	`fma-def_binary64`
161×	`associate-/l*_binary64`

Counts

71 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1282
1	280	1222
2	785	1160
3	2516	1148
4	4566	1139
5	5172	1139

prune35.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	39.7b	(.f64 (/.f64 (+.f64 x y) (-.f64 (pow.f64 x 3) (pow.f64 y 3))) (+.f64 (.f64 x x) (+.f64 (.f64 y y) (.f64 x y))))
	33.0b	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (-.f64 x y)))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

Compiler

Compiled 979 to 339 computations (65.4% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)

series32.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
16.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)

rewrite32.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
76×	`add-sqr-sqrt_binary64`
58×	`cbrt-prod_binary64`
52×	`cube-prod_binary64`

Counts

2 → 144

Calls

2 calls:

11.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)
7.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

simplify129.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

362×	`fma-def_binary64`
329×	`unswap-sqr_binary64`
285×	`distribute-rgt-in_binary64`
236×	`associate-/l/_binary64`
235×	`distribute-lft-in_binary64`

Counts

192 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	4190
1	648	3881
2	2075	3745
3	4846	3745
4	5066	3745

prune112.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	201	4	205

Error

Counts

205 → 4

Alt Table

Status	Error	Program
▶	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	33.0b	(*.f64 (sqrt.f64 (+.f64 x y)) (/.f64 (sqrt.f64 (+.f64 x y)) (-.f64 x y)))
	39.8b	(cbrt.f64 (/.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (-.f64 x y) 3)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

Compiler

Compiled 3808 to 1502 computations (60.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.5b	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

series26.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
9.0ms	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

simplify61.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-neg_binary64`
534×	`cancel-sign-sub-inv_binary64`
437×	`times-frac_binary64`
306×	`associate-/l*_binary64`
245×	`fma-def_binary64`

Counts

70 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1427
1	268	1315
2	845	1204
3	3551	1195
4	5024	1195

prune67.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Error

Counts

121 → 4

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
▶	1.0b	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3)))
	39.8b	(cbrt.f64 (/.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (-.f64 x y) 3)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

Compiler

Compiled 1957 to 809 computations (58.7% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
	0.5b	(expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
✓	0.5b	(pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3)
✓	0.5b	(cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3))

series108.0ms (5%)

Counts

2 → 48

Calls

2 calls:

87.0ms	(pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3)
20.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3))
2.0ms	(pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3)

simplify124.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

273×	`associate-+r+_binary64`
271×	`unswap-sqr_binary64`
242×	`fma-def_binary64`
188×	`+-commutative_binary64`
187×	`associate-+l+_binary64`

Counts

96 → 87

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	4646
1	765	4111
2	3016	3738
3	4709	3735
4	4953	3735

prune115.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	172	4	176

Error

Counts

176 → 4

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
✓	1.0b	(log1p.f64 (cbrt.f64 (pow.f64 (expm1.f64 (/.f64 (+.f64 x y) (-.f64 x y))) 3)))
	39.8b	(cbrt.f64 (/.f64 (pow.f64 (+.f64 x y) 3) (pow.f64 (-.f64 x y) 3)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

Compiler

Compiled 4452 to 2440 computations (45.2% saved)

regimes173.0ms (8%)

Accuracy

Total 0.0b remaining (49.6%)

Threshold costs 0.0b (49.6%)

Counts

48 → 1

Compiler

Compiled 1566 to 1122 computations (28.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end113.0ms (5.2%)

Compiler: Compiled 75 to 51 computations (32% saved)

Details

analyze35.0ms (1.6%)

sample789.0ms (36.4%)

simplify70.0ms (3.2%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite9.0ms (0.4%)

simplify92.0ms (4.2%)

prune35.0ms (1.6%)

localize6.0ms (0.3%)

series32.0ms (1.5%)

rewrite32.0ms (1.5%)

simplify129.0ms (5.9%)

prune112.0ms (5.2%)

localize8.0ms (0.3%)

series26.0ms (1.2%)

rewrite1.0ms (0.1%)

simplify61.0ms (2.8%)

prune67.0ms (3.1%)

localize9.0ms (0.4%)

series108.0ms (5%)

rewrite6.0ms (0.3%)

simplify124.0ms (5.7%)

prune115.0ms (5.3%)

regimes173.0ms (8%)

simplify3.0ms (0.1%)

end113.0ms (5.2%)

Profiling