Details

analyze16.0ms (0.5%)

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 (40.8%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify79.0ms (2.6%)

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 (0.1%)

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

21.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	20.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series26.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
7.0ms	(fma.f64 x x (*.f64 y y))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`frac-times_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

7.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify52.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

843×	`distribute-rgt-in_binary64`
815×	`distribute-lft-in_binary64`
413×	`times-frac_binary64`
413×	`fma-def_binary64`
73×	`cancel-sign-sub-inv_binary64`

Counts

89 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1667
1	332	1473
2	1320	1435
3	5254	1435

prune35.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	2	77

Error

0.0b

Counts

77 → 2

Alt Table

Status	Error	Program
✓	21.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 1708 to 448 computations (73.8% saved)

localize7.0ms (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 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series63.0ms (2%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
12.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
11.0ms	(hypot.f64 x y)
11.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite41.0ms (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:

12.0ms	(*.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))
5.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
0.0ms	(hypot.f64 x y)

simplify140.0ms (4.5%)

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

prune183.0ms (5.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	297	4	301
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	299	4	303

Error

Counts

303 → 4

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (cbrt.f64 (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log.f64 (exp.f64 (/.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))

Compiler

Compiled 7519 to 1950 computations (74.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
	0.0b	(hypot.f64 x y)
	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	1.2b	(log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

series51.0ms (1.6%)

Counts

1 → 24

Calls

1 calls:

51.0ms

(log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

simplify45.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

833×	`associate-/l*_binary64`
483×	`cancel-sign-sub-inv_binary64`
284×	`fma-neg_binary64`
282×	`associate-/r/_binary64`
226×	`sub-neg_binary64`

Counts

35 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1039
1	197	960
2	553	960
3	2060	960
4	5038	960

prune209.0ms (6.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	275	4	279

Error

Counts

279 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (cbrt.f64 (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log.f64 (exp.f64 (/.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))

Compiler

Compiled 7385 to 2564 computations (65.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series82.0ms (2.6%)

Counts

2 → 48

Calls

2 calls:

41.0ms	(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)
41.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

rewrite15.0ms (0.5%)

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:

10.0ms	(pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))) 3))

simplify66.0ms (2.1%)

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

prune204.0ms (6.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	285	4	289

Error

Counts

289 → 4

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	1.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 x y)) (cbrt.f64 (hypot.f64 x y)))) (*.f64 (/.f64 (-.f64 x y) (cbrt.f64 (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log.f64 (exp.f64 (/.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))

Compiler

Compiled 7809 to 2770 computations (64.5% saved)

regimes399.0ms (12.9%)

Accuracy

Total 0.0b remaining (51.2%)

Threshold costs 0.0b (51.2%)

Counts

145 → 1

Compiler

Compiled 8655 to 4948 computations (42.8% saved)

simplify2.0ms (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	11	26
1	15	26
2	20	26
3	22	26
4	23	26
5	23	26

end72.0ms (2.3%)

Compiler: Compiled 126 to 64 computations (49.2% saved)

Details

analyze16.0ms (0.5%)

sample1.3s (40.8%)

simplify79.0ms (2.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series26.0ms (0.9%)

rewrite10.0ms (0.3%)

simplify52.0ms (1.7%)

prune35.0ms (1.1%)

localize7.0ms (0.2%)

series63.0ms (2%)

rewrite41.0ms (1.3%)

simplify140.0ms (4.5%)

prune183.0ms (5.9%)

localize11.0ms (0.3%)

series51.0ms (1.6%)

rewrite1.0ms (0%)

simplify45.0ms (1.5%)

prune209.0ms (6.8%)

localize10.0ms (0.3%)

series82.0ms (2.6%)

rewrite15.0ms (0.5%)

simplify66.0ms (2.1%)

prune204.0ms (6.6%)

regimes399.0ms (12.9%)

simplify2.0ms (0.1%)

end72.0ms (2.3%)

Profiling