Details

analyze489.0ms (9.4%)

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
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.3s (24.6%)

Results

1000.0ms	8256×	body	128	valid
136.0ms	1216×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify61.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	2.8b	(*.f64 (/.f64 x y) z)

series36.0ms (0.7%)

Counts

3 → 96

Calls

3 calls:

19.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
12.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

7.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
4.0ms	(*.f64 (/.f64 x y) z)
4.0ms	(/.f64 (+.f64 x 4) y)

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune195.0ms (3.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Error

Counts

179 → 8

Alt Table

Status	Error	Program
	3.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
	29.5b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	2.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
▶	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 z x) y)) (cbrt.f64 (/.f64 (.f64 z x) y))) (cbrt.f64 (/.f64 (*.f64 z x) y)))))
	13.2b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 3828 to 1820 computations (52.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
✓	0.0b	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z))
	2.8b	(*.f64 (/.f64 x y) z)

series28.0ms (0.5%)

Counts

2 → 57

Calls

2 calls:

21.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z))
7.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`fma-def_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`

Counts

2 → 57

Calls

2 calls:

7.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z))
7.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

444×	`fma-def_binary64`
442×	`associate-l_binary64`
409×	`associate-r_binary64`
329×	`distribute-rgt-in_binary64`
305×	`distribute-lft-in_binary64`

Counts

114 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1890
1	318	1799
2	1069	1342
3	4351	1342
4	4995	1342
5	4939	1342

prune155.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	153	8	161

Error

Counts

161 → 8

Alt Table

Status	Error	Program
	3.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
	29.5b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
	2.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
✓	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 z x) y)) (cbrt.f64 (/.f64 (.f64 z x) y))) (cbrt.f64 (/.f64 (*.f64 z x) y)))))
	13.2b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 3796 to 1801 computations (52.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	1.1b	(*.f64 (/.f64 x (cbrt.f64 y)) z)
✓	3.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))

series718.0ms (13.8%)

Counts

4 → 96

Calls

4 calls:

606.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) z)
40.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))
39.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
45×	`add-sqr-sqrt_binary64`
35×	`associate-l_binary64`
35×	`add-cbrt-cube_binary64`

Counts

4 → 152

Calls

4 calls:

13.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))
6.0ms	(*.f64 (/.f64 x (cbrt.f64 y)) z)
5.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify123.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
610×	`associate-/l/_binary64`
454×	`*-commutative_binary64`
384×	`unswap-sqr_binary64`
192×	`associate-r_binary64`

Counts

248 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3394
1	393	2332
2	1491	2271
3	2499	2256
4	4837	2256
5	5214	2256

prune270.0ms (5.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	260	8	268

Error

Counts

268 → 8

Alt Table

Status	Error	Program
	3.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
	29.5b	(fabs.f64 (*.f64 (-.f64 (/.f64 1 y) (/.f64 z y)) x))
▶	2.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	13.2b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 x z)) (cbrt.f64 y))))
✓	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 (/.f64 x (cbrt.f64 y)) z))))
✓	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 7226 to 3054 computations (57.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (fma.f64 x z -4))
✓	2.2b	(/.f64 (-.f64 x (fma.f64 x z -4)) y)

series20.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

15.0ms	(/.f64 (-.f64 x (fma.f64 x z -4)) y)
4.0ms	(-.f64 x (fma.f64 x z -4))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
9×	`prod-diff_binary64`

Counts

2 → 71

Calls

2 calls:

4.0ms	(/.f64 (-.f64 x (fma.f64 x z -4)) y)
3.0ms	(-.f64 x (fma.f64 x z -4))

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-neg_binary64`
446×	`associate-l_binary64`
420×	`div-sub_binary64`
358×	`associate-r_binary64`
297×	`fma-def_binary64`

Counts

131 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	2146
1	314	2027
2	864	1648
3	3571	1648
4	4943	1648

prune123.0ms (2.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	126	7	133

Error

Counts

133 → 7

Alt Table

Status	Error	Program
	3.0b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 (cbrt.f64 x) y) z))))
✓	2.3b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	13.2b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (/.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 x z)) (cbrt.f64 y))))
✓	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
	2.4b	(fabs.f64 (/.f64 1 (/.f64 y (-.f64 x (fma.f64 x z -4)))))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 2396 to 1458 computations (39.1% saved)

regimes1.2s (22.9%)

Accuracy

Total 0.1b remaining (92.1%)

Threshold costs 0.1b (92.1%)

Counts

104 → 2

Compiler

Compiled 9468 to 6382 computations (32.6% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	57
1	40	57
2	60	57
3	78	57
4	94	57
5	101	57
6	102	57
7	99	57

end103.0ms (2%)

Compiler: Compiled 215 to 134 computations (37.7% saved)

Details

analyze489.0ms (9.4%)

sample1.3s (24.6%)

simplify61.0ms (1.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series36.0ms (0.7%)

rewrite23.0ms (0.4%)

simplify116.0ms (2.2%)

prune195.0ms (3.8%)

localize9.0ms (0.2%)

series28.0ms (0.5%)

rewrite17.0ms (0.3%)

simplify87.0ms (1.7%)

prune155.0ms (3%)

localize13.0ms (0.2%)

series718.0ms (13.8%)

rewrite36.0ms (0.7%)

simplify123.0ms (2.4%)

prune270.0ms (5.2%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify78.0ms (1.5%)

prune123.0ms (2.4%)

regimes1.2s (22.9%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end103.0ms (2%)

Profiling