Details

analyze7.0ms (0.1%)

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
9.4%	9.4%	81.3%	3
9.4%	9.4%	81.3%	4
16.4%	2.3%	81.3%	5
16.4%	2.3%	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)

sample1.5s (27.7%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify110.0ms (2%)

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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

18.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize18.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	18.3b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series37.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

37.0ms

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

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`frac-times_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

17.0ms

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

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

801×	`distribute-rgt-in_binary64`
770×	`distribute-lft-in_binary64`
413×	`times-frac_binary64`
375×	`fma-def_binary64`
71×	`cancel-sign-sub-inv_binary64`

Counts

55 → 60

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1375
1	328	1210
2	1274	1172
3	5121	1172

prune82.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	4	61

Error

0.0b

Counts

61 → 4

Alt Table

Status	Error	Program
✓	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	18.6b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	44.0b	1

Compiler

Compiled 1491 to 429 computations (71.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	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)))

series119.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

52.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
29.0ms	(hypot.f64 x y)
20.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
18.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

rewrite73.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 146

Calls

4 calls:

30.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
8.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
8.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
1.0ms	(hypot.f64 x y)

simplify370.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

776×	`times-frac_binary64`
614×	`fma-neg_binary64`
593×	`fma-def_binary64`
222×	`sub-neg_binary64`
164×	`associate-*l/_binary64`

Counts

242 → 259

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	5087
1	854	4676
2	2705	4565
3	4842	4565
4	5181	4565

prune437.0ms (8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	300	5	305

Error

Counts

305 → 5

Alt Table

Status	Error	Program
▶	0.0b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))
✓	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	18.6b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	0.1b	(.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))) (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

Compiler

Compiled 7541 to 1950 computations (74.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series137.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

75.0ms	(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)
61.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
8×	`cbrt-prod_binary64`
6×	`cube-div_binary64`
5×	`rem-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

21.0ms	(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

simplify124.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

422×	`associate-*l/_binary64`
398×	`times-frac_binary64`
277×	`associate-/l*_binary64`
227×	`distribute-rgt-in_binary64`
218×	`distribute-lft-in_binary64`

Counts

103 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2611
1	391	2373
2	1262	2281
3	5121	2281

prune386.0ms (7.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	262	5	267

Error

Counts

267 → 5

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))
✓	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	18.6b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
▶	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	0.1b	(.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))) (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

Compiler

Compiled 7128 to 2280 computations (68% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series91.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

49.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
24.0ms	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
17.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

rewrite138.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

275×	`times-frac_binary64`
211×	`add-sqr-sqrt_binary64`
188×	`*-un-lft-identity_binary64`
128×	`add-cube-cbrt_binary64`
68×	`associate-l_binary64`

Counts

3 → 277

Calls

3 calls:

35.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
14.0ms	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
8.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

simplify353.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

638×	`distribute-rgt-in_binary64`
457×	`fma-def_binary64`
186×	`associate-*l/_binary64`
175×	`associate-r_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

349 → 439

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	8487
1	810	7567
2	2955	7421
3	5314	7421

prune601.0ms (11%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	500	0	500
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	500	5	505

Error

Counts

505 → 5

Alt Table

Status	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))
✓	18.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	18.6b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	0.1b	(.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (*.f64 (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))) (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))) (cbrt.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

Compiler

Compiled 14037 to 3577 computations (74.5% saved)

regimes483.0ms (8.9%)

Accuracy

Total 0.0b remaining (67.6%)

Threshold costs 0.0b (67.6%)

Counts

100 → 1

Compiler

Compiled 5679 to 3055 computations (46.2% saved)

simplify3.0ms (0.1%)

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	12	27
1	16	27
2	21	27
3	23	27
4	24	27
5	24	27

end145.0ms (2.7%)

Compiler: Compiled 147 to 70 computations (52.4% saved)

Details

analyze7.0ms (0.1%)

sample1.5s (27.7%)

simplify110.0ms (2%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

series37.0ms (0.7%)

rewrite23.0ms (0.4%)

simplify99.0ms (1.8%)

prune82.0ms (1.5%)

localize16.0ms (0.3%)

series119.0ms (2.2%)

rewrite73.0ms (1.3%)

simplify370.0ms (6.8%)

prune437.0ms (8%)

localize24.0ms (0.4%)

series137.0ms (2.5%)

rewrite32.0ms (0.6%)

simplify124.0ms (2.3%)

prune386.0ms (7.1%)

localize19.0ms (0.4%)

series91.0ms (1.7%)

rewrite138.0ms (2.5%)

simplify353.0ms (6.5%)

prune601.0ms (11%)

regimes483.0ms (8.9%)

simplify3.0ms (0.1%)

end145.0ms (2.7%)

Profiling