Details

analyze19.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.3s (23.6%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

917×	`times-frac_binary64`
816×	`unsub-neg_binary64`
772×	`fma-def_binary64`
484×	`fma-neg_binary64`
376×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	55	20
3	112	20
4	271	20
5	657	20
6	1234	20
7	2620	20
8	3288	20
9	4652	20
10	5075	20

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

20.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

Compiler

Compiled 65 to 29 computations (55.4% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	20.3b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

series27.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
7.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`flip-+_binary64`
5×	`flip3-+_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

949×	`distribute-rgt-in_binary64`
893×	`distribute-lft-in_binary64`
607×	`fma-def_binary64`
132×	`cancel-sign-sub-inv_binary64`
127×	`div-sub_binary64`

Counts

95 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	124	1718
1	414	1552
2	1742	1514
3	5985	1514

prune63.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	3	103

Error

0.0b

Counts

103 → 3

Alt Table

Status	Error	Program
	20.5b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
	20.5b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (-.f64 x y) (+.f64 x y))))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 2452 to 586 computations (76.1% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series49.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
11.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
10.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

3 → 136

Calls

3 calls:

13.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
6.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
5.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
493×	`distribute-rgt-in_binary64`
464×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
176×	`sub-neg_binary64`

Counts

208 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4519
1	735	4135
2	2321	4033
3	5136	4033

prune167.0ms (3.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	213	3	216
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	215	4	219

Error

Counts

219 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
	20.5b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (-.f64 x y) (+.f64 x y))))
	0.0b	(*.f64 (-.f64 (/.f64 x (hypot.f64 x y)) (/.f64 y (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
▶	0.0b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))

Compiler

Compiled 5497 to 1169 computations (78.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series130.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

54.0ms

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

41.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))

36.0ms

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

rewrite495.0ms (9%)

Algorithm

1×	rewrite-expression-head

Rules

1165×	`add-cbrt-cube_binary64`
1126×	`add-exp-log_binary64`
636×	`cbrt-unprod_binary64`
624×	`prod-exp_binary64`
356×	`cbrt-undiv_binary64`

Counts

3 → 552

Calls

3 calls:

50.0ms

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

34.0ms

(cbrt.f64 (*.f64 (*.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))

21.0ms

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

simplify564.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
505×	`associate-/l*_binary64`
406×	`associate-*r/_binary64`
391×	`*-commutative_binary64`
344×	`times-frac_binary64`

Counts

624 → 594

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	629	52334
1	1022	16876
2	2222	14596
3	4539	14572
4	5215	14572

prune708.0ms (12.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	864	0	864
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	864	4	868

Error

Counts

868 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
	20.5b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (-.f64 x y) (+.f64 x y))))
▶	0.0b	(*.f64 (-.f64 (/.f64 x (hypot.f64 x y)) (/.f64 y (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	0.0b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))

Compiler

Compiled 58621 to 4277 computations (92.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series88.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

52.0ms	(*.f64 (-.f64 (/.f64 x (hypot.f64 x y)) (/.f64 y (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
22.0ms	(/.f64 y (hypot.f64 x y))
13.0ms	(-.f64 (/.f64 x (hypot.f64 x y)) (/.f64 y (hypot.f64 x y)))

rewrite86.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64`
249×	`add-sqr-sqrt_binary64`
242×	`*-un-lft-identity_binary64`
220×	`add-cube-cbrt_binary64`
169×	`prod-diff_binary64`

Counts

3 → 302

Calls

3 calls:

21.0ms	(*.f64 (-.f64 (/.f64 x (hypot.f64 x y)) (/.f64 y (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
15.0ms	(-.f64 (/.f64 x (hypot.f64 x y)) (/.f64 y (hypot.f64 x y)))
2.0ms	(/.f64 y (hypot.f64 x y))

simplify332.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

870×	`times-frac_binary64`
232×	`fma-neg_binary64`
188×	`associate-*r/_binary64`
177×	`*-commutative_binary64`
156×	`fma-udef_binary64`

Counts

374 → 418

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	19094
1	1224	11812
2	3323	11306
3	4980	11306

prune436.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	477	1	478
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	479	3	482

Error

Counts

482 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 (-.f64 (/.f64 x (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 y (hypot.f64 x y))))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	20.5b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 (-.f64 x y) (+.f64 x y))))
✓	0.0b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))

Compiler

Compiled 20852 to 3580 computations (82.8% saved)

regimes629.0ms (11.5%)

Accuracy

Total 0.0b remaining (46.8%)

Threshold costs 0.0b (46.8%)

Counts

219 → 1

Compiler

Compiled 16071 to 7416 computations (53.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	17	25
2	21	25
3	23	25
4	24	25
5	23	25

end61.0ms (1.1%)

Compiler: Compiled 130 to 53 computations (59.2% saved)

Details

analyze19.0ms (0.4%)

sample1.3s (23.6%)

simplify77.0ms (1.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series27.0ms (0.5%)

rewrite17.0ms (0.3%)

simplify57.0ms (1%)

prune63.0ms (1.1%)

localize8.0ms (0.2%)

series49.0ms (0.9%)

rewrite34.0ms (0.6%)

simplify103.0ms (1.9%)

prune167.0ms (3.1%)

localize11.0ms (0.2%)

series130.0ms (2.4%)

rewrite495.0ms (9%)

simplify564.0ms (10.3%)

prune708.0ms (12.9%)

localize9.0ms (0.2%)

series88.0ms (1.6%)

rewrite86.0ms (1.6%)

simplify332.0ms (6.1%)

prune436.0ms (8%)

regimes629.0ms (11.5%)

simplify2.0ms (0%)

end61.0ms (1.1%)

Profiling