Details

analyze43.0ms (1.8%)

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
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample108.0ms (4.4%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify66.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
365×	`times-frac_binary64`
331×	`div-sub_binary64`
156×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	52	10
5	81	10
6	124	10
7	191	10
8	300	10
9	641	10
10	822	10
11	1299	10
12	1328	10
13	1343	10
14	1357	10
15	1377	10
16	1377	10
17	1276	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)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

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

rewrite13.0ms (0.5%)

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 → 48

Calls

1 calls:

10.0ms

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

simplify75.0ms (3%)

Algorithm

1×	egg-herbie

Rules

610×	`div-sub_binary64`
586×	`fma-neg_binary64`
530×	`cancel-sign-sub-inv_binary64`
194×	`distribute-neg-frac_binary64`
184×	`fma-def_binary64`

Counts

72 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1287
1	283	1239
2	748	1195
3	2488	1183
4	4383	1183
5	5485	1183

prune44.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	5	60

Error

Counts

60 → 5

Alt Table

Status	Error	Program
▶	0.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
	31.9b	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
	30.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
	32.1b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 1039 to 344 computations (66.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
✓	2.9b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y)))

series30.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
15.0ms	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

simplify66.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-neg_binary64`
394×	`sub-neg_binary64`
355×	`distribute-neg-frac_binary64`
205×	`times-frac_binary64`
180×	`associate-+l+_binary64`

Counts

70 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1295
1	264	1219
2	813	1159
3	3385	1147
4	5110	1147

prune92.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Status	Error	Program
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
	31.9b	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
▶	30.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
	32.1b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 2339 to 938 computations (59.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
✓	2.1b	(-.f64 (.f64 x x) (.f64 y y))
✓	29.5b	(/.f64 (-.f64 x y) (-.f64 (.f64 x x) (.f64 y y)))

series31.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
10.0ms	(/.f64 (-.f64 x y) (-.f64 (.f64 x x) (.f64 y y)))
6.0ms	(-.f64 (.f64 x x) (.f64 y y))

rewrite36.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
41×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`

Counts

3 → 144

Calls

3 calls:

12.0ms	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
6.0ms	(/.f64 (-.f64 x y) (-.f64 (.f64 x x) (.f64 y y)))
3.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify161.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
345×	`exp-prod_binary64`
342×	`cancel-sign-sub-inv_binary64`
240×	`fma-neg_binary64`
200×	`associate-r_binary64`

Counts

216 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	4869
1	641	3929
2	2547	3580
3	4551	3580
4	4905	3580
5	5002	3580

prune114.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	235	0	235
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	235	5	240

Error

Counts

240 → 5

Alt Table

Status	Error	Program
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
▶	31.9b	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
✓	30.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
	32.1b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 5936 to 1157 computations (80.5% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3))
✓	0.2b	(pow.f64 (/.f64 y x) 3)
✓	0.2b	(*.f64 (/.f64 y x) (/.f64 y x))
✓	7.6b	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))

series92.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

30.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
29.0ms	(+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3))
17.0ms	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
15.0ms	(pow.f64 (/.f64 y x) 3)

rewrite39.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

4 → 158

Calls

4 calls:

20.0ms	(+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3))
7.0ms	(*.f64 (/.f64 y x) (/.f64 y x))
3.0ms	(pow.f64 (/.f64 y x) 3)
0.0ms	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))

simplify135.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

768×	`fma-def_binary64`
713×	`fma-neg_binary64`
314×	`log-prod_binary64`
260×	`exp-prod_binary64`
252×	`associate-r_binary64`

Counts

254 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	3518
1	596	2984
2	2633	2908
3	3939	2854
4	4957	2854
5	5036	2854

prune150.0ms (6.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	219	5	224

Error

Counts

224 → 5

Alt Table

Status	Error	Program
✓	0.8b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
✓	31.9b	(fma.f64 -2 (+.f64 (/.f64 y x) (pow.f64 (/.f64 y x) 3)) (fma.f64 2 (*.f64 (/.f64 y x) (/.f64 y x)) 1))
✓	30.8b	(.f64 (/.f64 (-.f64 x y) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
	32.1b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 6111 to 2574 computations (57.9% saved)

regimes256.0ms (10.4%)

Accuracy

Total 0.0b remaining (73.4%)

Threshold costs 0.0b (73.4%)

Counts

94 → 1

Compiler

Compiled 4542 to 2777 computations (38.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	16	16
2	21	16
3	24	16
4	25	16
5	25	16

end0.0ms (0%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

sample863.0ms (35.2%)

Algorithm

1×

intervals

Results

236.0ms

8000×

body

128

valid

Compiler

Compiled 107 to 57 computations (46.7% saved)

Details

analyze43.0ms (1.8%)

sample108.0ms (4.4%)

simplify66.0ms (2.7%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.3%)

rewrite13.0ms (0.5%)

simplify75.0ms (3%)

prune44.0ms (1.8%)

localize7.0ms (0.3%)

series30.0ms (1.2%)

rewrite1.0ms (0.1%)

simplify66.0ms (2.7%)

prune92.0ms (3.7%)

localize7.0ms (0.3%)

series31.0ms (1.3%)

rewrite36.0ms (1.4%)

simplify161.0ms (6.6%)

prune114.0ms (4.7%)

localize9.0ms (0.4%)

series92.0ms (3.8%)

rewrite39.0ms (1.6%)

simplify135.0ms (5.5%)

prune150.0ms (6.1%)

regimes256.0ms (10.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample863.0ms (35.2%)

Profiling