Details

analyze96.0ms (1.7%)

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
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 20 to 10 computations (50% saved)

sample126.0ms (2.2%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 41 to 21 computations (48.8% saved)

simplify138.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

985×	`associate-/l*_binary64`
659×	`distribute-lft-out_binary64`
601×	`*-commutative_binary64`
469×	`distribute-rgt-out_binary64`
356×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	39	25
2	135	23
3	474	23
4	1536	23
5	2122	23
6	2589	23
7	2567	23
8	2620	23
9	2677	23
10	2770	23
11	3956	23
12	4088	23
13	4454	23
14	4983	23
15	4968	23
16	4961	23

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

24.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	24.8b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
▶	24.8b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 109 to 47 computations (56.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.1b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
✓	24.5b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

series70.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

52.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
12.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
5.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip-+_binary64`
60×	`frac-times_binary64`
60×	`flip3-+_binary64`
31×	`add-cbrt-cube_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 146

Calls

3 calls:

14.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
13.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
6.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify108.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

650×	`times-frac_binary64`
389×	`fma-def_binary64`
369×	`distribute-rgt-in_binary64`
363×	`associate-/l*_binary64`
348×	`distribute-lft-in_binary64`

Counts

218 → 276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	448	7281
1	1472	6637
2	5162	6637

prune207.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	269	7	276
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	270	8	278

Error

2.8b

Counts

278 → 8

Alt Table

Status	Error	Program
	35.4b	(/.f64 y (*.f64 (+.f64 1 x) x))
	24.8b	(.f64 (.f64 x y) (/.f64 1 (.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))))
	24.9b	(/.f64 1 (/.f64 (.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) (*.f64 x y)))
	47.4b	(exp.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 y)) (+.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 (+.f64 x y))) (log.f64 (+.f64 (+.f64 x y) 1)))))
	24.8b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	20.3b	(/.f64 (/.f64 (.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (+.f64 (+.f64 x y) 1))
	9.8b	(/.f64 x (/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))))
▶	9.3b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))

Compiler

Compiled 10320 to 4330 computations (58% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))))
✓	4.8b	(/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
✓	8.2b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))

series248.0ms (4.4%)

Counts

4 → 96

Calls

4 calls:

133.0ms	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
59.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))))
46.0ms	(/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
9.0ms	(/.f64 x (+.f64 x y))

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

167×	`*-un-lft-identity_binary64`
82×	`times-frac_binary64`
81×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
49×	`distribute-lft-out_binary64`

Counts

4 → 251

Calls

4 calls:

31.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y)))))
26.0ms	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))) (-.f64 (+.f64 x y) 1))
13.0ms	(/.f64 y (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
3.0ms	(/.f64 x (+.f64 x y))

simplify269.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-def_binary64`
640×	`times-frac_binary64`
242×	`+-commutative_binary64`
223×	`*-commutative_binary64`
175×	`associate-+r+_binary64`

Counts

347 → 446

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	840	15636
1	2769	14225
2	4985	14224
3	4983	14224

prune530.0ms (9.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	444	2	446
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	447	7	454

Error

2.8b

Counts

454 → 7

Alt Table

Status	Error	Program
	35.4b	(/.f64 y (*.f64 (+.f64 1 x) x))
	13.9b	(/.f64 (.f64 (.f64 (/.f64 x (+.f64 x y)) y) (-.f64 (+.f64 x y) 1)) (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
	24.9b	(/.f64 1 (/.f64 (.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) (*.f64 x y)))
	47.4b	(exp.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 y)) (+.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 (+.f64 x y))) (log.f64 (+.f64 (+.f64 x y) 1)))))
	20.3b	(/.f64 (/.f64 (.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (+.f64 (+.f64 x y) 1))
	9.8b	(/.f64 x (/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))))
▶	9.3b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))) (-.f64 (+.f64 x y) 1))

Compiler

Compiled 22510 to 11049 computations (50.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(*.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))))
✓	4.8b	(/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))
✓	8.2b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))) (-.f64 (+.f64 x y) 1))

series222.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

118.0ms

(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))) (-.f64 (+.f64 x y) 1))

58.0ms

(*.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))))

46.0ms

(/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`*-un-lft-identity_binary64`
82×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64`
24×	`prod-diff_binary64`

Counts

3 → 172

Calls

3 calls:

14.0ms

(*.f64 (*.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))) (-.f64 (+.f64 x y) 1))

10.0ms

(/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))

7.0ms

(*.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x))))))

simplify250.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
553×	`times-frac_binary64`
235×	`+-commutative_binary64`
190×	`*-commutative_binary64`
175×	`associate-+r+_binary64`

Counts

244 → 301

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	806	13442
1	2546	12250
2	4902	12157
3	4975	12157

prune458.0ms (8.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	369	0	369
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	369	7	376

Error

2.8b

Counts

376 → 7

Alt Table

Status	Error	Program
	35.4b	(/.f64 y (*.f64 (+.f64 1 x) x))
	13.9b	(/.f64 (.f64 (.f64 (/.f64 x (+.f64 x y)) y) (-.f64 (+.f64 x y) 1)) (+.f64 (pow.f64 (+.f64 x y) 3) (neg.f64 (+.f64 x y))))
	24.9b	(/.f64 1 (/.f64 (.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)) (*.f64 x y)))
	47.4b	(exp.f64 (-.f64 (+.f64 (log.f64 x) (log.f64 y)) (+.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 (+.f64 x y))) (log.f64 (+.f64 (+.f64 x y) 1)))))
	20.3b	(/.f64 (/.f64 (.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (+.f64 (+.f64 x y) 1))
▶	9.8b	(/.f64 x (/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))))
✓	9.3b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))) (-.f64 (+.f64 x y) 1))

Compiler

Compiled 19771 to 10579 computations (46.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.0b	(/.f64 y (+.f64 x (+.f64 y 1)))
✓	4.5b	(/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1))))
✓	5.1b	(/.f64 x (/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))))

series78.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

50.0ms	(/.f64 x (/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))))
16.0ms	(/.f64 y (+.f64 x (+.f64 y 1)))
12.0ms	(/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1))))

rewrite63.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
208×	`*-un-lft-identity_binary64`
98×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
66×	`distribute-lft-out_binary64`

Counts

3 → 241

Calls

3 calls:

14.0ms	(/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1))))
13.0ms	(/.f64 x (/.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (/.f64 y (+.f64 x (+.f64 y 1)))))
5.0ms	(/.f64 y (+.f64 x (+.f64 y 1)))

simplify170.0ms (3%)

Algorithm

1×	egg-herbie

Rules

391×	`associate-/r*_binary64`
384×	`times-frac_binary64`
307×	`associate-/l*_binary64`
307×	`fma-def_binary64`
301×	`associate-/r/_binary64`

Counts

313 → 369

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	623	11358
1	1731	10717
2	4984	10717

prune527.0ms (9.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	412	8	420
Fresh	5	0	5
Picked	1	0	1
Done	0	1	1
Total	418	9	427

Error

0.1b

Counts

427 → 9

Alt Table

Status	Error	Program
	13.8b	(/.f64 (/.f64 x (/.f64 (+.f64 x y) (sqrt.f64 (/.f64 y (+.f64 x (+.f64 y 1)))))) (/.f64 (+.f64 x y) (sqrt.f64 (/.f64 y (+.f64 x (+.f64 y 1))))))
	20.4b	(.f64 (/.f64 1 (/.f64 (+.f64 x y) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (sqrt.f64 (+.f64 x (+.f64 y 1)))))) (/.f64 x (/.f64 (+.f64 x y) (/.f64 (cbrt.f64 y) (sqrt.f64 (+.f64 x (+.f64 y 1)))))))
	0.5b	(/.f64 (/.f64 x (+.f64 x y)) (/.f64 (+.f64 x y) (/.f64 y (+.f64 x (+.f64 y 1)))))
	0.5b	(*.f64 (/.f64 1 (+.f64 x y)) (/.f64 x (/.f64 (+.f64 x y) (/.f64 y (+.f64 x (+.f64 y 1))))))
	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (+.f64 x y) (*.f64 (cbrt.f64 (/.f64 y (+.f64 x (+.f64 y 1)))) (cbrt.f64 (/.f64 y (+.f64 x (+.f64 y 1))))))) (/.f64 (cbrt.f64 x) (/.f64 (+.f64 x y) (cbrt.f64 (/.f64 y (+.f64 x (+.f64 y 1)))))))
✓	9.3b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (-.f64 (pow.f64 (+.f64 y x) 3) (+.f64 y x)))))) (-.f64 (+.f64 x y) 1))
	14.6b	(/.f64 (/.f64 x (/.f64 (+.f64 x y) (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (+.f64 x (+.f64 y 1))) (cbrt.f64 (+.f64 x (+.f64 y 1))))))) (/.f64 (+.f64 x y) (/.f64 (sqrt.f64 y) (cbrt.f64 (+.f64 x (+.f64 y 1))))))
	7.3b	(.f64 (/.f64 1 (/.f64 (+.f64 x y) (/.f64 y (-.f64 (.f64 x x) (*.f64 (+.f64 y 1) (+.f64 y 1)))))) (/.f64 x (/.f64 (+.f64 x y) (-.f64 x (+.f64 y 1)))))
	10.2b	(/.f64 x (/.f64 (.f64 (.f64 (+.f64 x y) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (cbrt.f64 (+.f64 x y))) (/.f64 y (+.f64 x (+.f64 y 1)))))

Compiler

Compiled 13414 to 6497 computations (51.6% saved)

regimes903.0ms (16.1%)

Accuracy

Total 0.4b remaining (89.8%)

Threshold costs 0.4b (89.8%)

Counts

250 → 1

Compiler

Compiled 17982 to 10129 computations (43.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	16	25
2	15	25

end6.0ms (0.1%)

Compiler: Compiled 57 to 30 computations (47.4% saved)

sample904.0ms (16.1%)

Algorithm

1×

intervals

Results

374.0ms

8000×

body

128

valid

Compiler

Compiled 319 to 179 computations (43.9% saved)

Details

analyze96.0ms (1.7%)

sample126.0ms (2.2%)

simplify138.0ms (2.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series70.0ms (1.2%)

rewrite50.0ms (0.9%)

simplify108.0ms (1.9%)

prune207.0ms (3.7%)

localize10.0ms (0.2%)

series248.0ms (4.4%)

rewrite104.0ms (1.8%)

simplify269.0ms (4.8%)

prune530.0ms (9.4%)

localize13.0ms (0.2%)

series222.0ms (3.9%)

rewrite51.0ms (0.9%)

simplify250.0ms (4.4%)

prune458.0ms (8.1%)

localize8.0ms (0.1%)

series78.0ms (1.4%)

rewrite63.0ms (1.1%)

simplify170.0ms (3%)

prune527.0ms (9.4%)

regimes903.0ms (16.1%)

simplify2.0ms (0%)

end6.0ms (0.1%)

sample904.0ms (16.1%)

Profiling