Details

analyze511.0ms (8%)

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 (20%)

Results

1.0s	8256×	body	128	valid
143.0ms	1255×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify62.0ms (1%)

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
	2.8b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	1.0b	(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 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	2.7b	(*.f64 (/.f64 x y) z)

series40.0ms (0.6%)

Counts

3 → 96

Calls

3 calls:

22.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
13.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

rewrite24.0ms (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:

9.0ms	(-.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)

simplify118.0ms (1.8%)

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

prune161.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Error

Counts

179 → 6

Alt Table

Status	Error	Program
	2.1b	(fabs.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (.f64 (/.f64 x y) z))))
	11.5b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	32.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))
	3.9b	(fabs.f64 (+.f64 (-.f64 (/.f64 (+.f64 x 4) (pow.f64 (cbrt.f64 y) 3)) (/.f64 (*.f64 z x) y)) 0))
▶	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 3752 to 1799 computations (52.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	0.8b	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	2.2b	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))

series756.0ms (11.8%)

Counts

4 → 96

Calls

4 calls:

666.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
36.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
28.0ms	(cbrt.f64 z)
25.0ms	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64`
33×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`

Counts

4 → 123

Calls

4 calls:

9.0ms	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
8.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

807×	`unswap-sqr_binary64`
622×	`associate-*l/_binary64`
554×	`*-commutative_binary64`
396×	`associate-*r/_binary64`
354×	`associate-/l*_binary64`

Counts

219 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	2506
1	333	2092
2	1282	1957
3	3491	1929
4	4944	1929
5	4942	1929

prune171.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	219	6	225

Error

Counts

225 → 6

Alt Table

Status	Error	Program
▶	2.1b	(fabs.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (.f64 (/.f64 x y) z))))
	11.5b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	32.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))
	3.9b	(fabs.f64 (+.f64 (-.f64 (/.f64 (+.f64 x 4) (pow.f64 (cbrt.f64 y) 3)) (/.f64 (*.f64 z x) y)) 0))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 5438 to 2233 computations (58.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (.f64 (/.f64 x y) z)))
✓	0.6b	(*.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y)))
✓	0.6b	(cbrt.f64 (/.f64 (+.f64 x 4) y))
	2.7b	(*.f64 (/.f64 x y) z)

series1.1s (17.5%)

Counts

3 → 84

Calls

3 calls:

549.0ms

(fma.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (*.f64 (/.f64 x y) z)))

338.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y)))

234.0ms

(cbrt.f64 (/.f64 (+.f64 x 4) y))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`cbrt-prod_binary64`
99×	`*-un-lft-identity_binary64`
78×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
51×	`add-cube-cbrt_binary64`

Counts

3 → 132

Calls

3 calls:

17.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y)))

3.0ms

(cbrt.f64 (/.f64 (+.f64 x 4) y))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (*.f64 (/.f64 x y) z)))

simplify180.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-def_binary64`
556×	`fma-neg_binary64`
183×	`times-frac_binary64`
172×	`cancel-sign-sub-inv_binary64`
171×	`associate-/l*_binary64`

Counts

216 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	315	6621
1	717	6183
2	1920	5430
3	4707	5420
4	5133	5420

prune411.0ms (6.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	480	0	480
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	480	6	486

Error

Counts

486 → 6

Alt Table

Status	Error	Program
✓	2.1b	(fabs.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (.f64 (/.f64 x y) z))))
	11.5b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	32.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))
	3.9b	(fabs.f64 (+.f64 (-.f64 (/.f64 (+.f64 x 4) (pow.f64 (cbrt.f64 y) 3)) (/.f64 (*.f64 z x) y)) 0))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
▶	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 18193 to 11143 computations (38.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x 4) y)
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
✓	0.2b	(*.f64 (/.f64 1 y) z)
✓	6.6b	(.f64 x (.f64 (/.f64 1 y) z))

series37.0ms (0.6%)

Counts

3 → 96

Calls

3 calls:

17.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
14.0ms	(.f64 x (.f64 (/.f64 1 y) z))
5.0ms	(*.f64 (/.f64 1 y) z)

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
35×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`

Counts

3 → 110

Calls

3 calls:

8.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z)))
8.0ms	(.f64 x (.f64 (/.f64 1 y) z))
5.0ms	(*.f64 (/.f64 1 y) z)

simplify113.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
405×	`fma-neg_binary64`
334×	`associate-*l/_binary64`
312×	`cancel-sign-sub-inv_binary64`
299×	`*-commutative_binary64`

Counts

206 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2789
1	410	2567
2	1204	1918
3	3298	1906
4	4681	1906
5	4856	1906

prune182.0ms (2.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	215	6	221

Error

Counts

221 → 6

Alt Table

Status	Error	Program
✓	2.1b	(fabs.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x 4) y)) (cbrt.f64 (/.f64 (+.f64 x 4) y))) (cbrt.f64 (/.f64 (+.f64 x 4) y)) (neg.f64 (.f64 (/.f64 x y) z))))
	11.5b	(fabs.f64 (-.f64 (/.f64 (-.f64 (.f64 x x) (.f64 4 4)) (.f64 y (-.f64 x 4))) (.f64 (/.f64 x y) z)))
	32.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (/.f64 x (sqrt.f64 y)) z))))
	3.9b	(fabs.f64 (+.f64 (-.f64 (/.f64 (+.f64 x 4) (pow.f64 (cbrt.f64 y) 3)) (/.f64 (*.f64 z x) y)) 0))
✓	1.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))

Compiler

Compiled 4609 to 2817 computations (38.9% saved)

regimes894.0ms (13.9%)

Accuracy

Total 0.7b remaining (97.5%)

Threshold costs 0.7b (97.5%)

Counts

176 → 1

Compiler

Compiled 18158 to 12332 computations (32.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	27	42
2	41	42
3	63	42
4	85	42
5	99	42
6	105	42
7	106	42
8	105	42

end96.0ms (1.5%)

Compiler: Compiled 191 to 123 computations (35.6% saved)

Details

analyze511.0ms (8%)

sample1.3s (20%)

simplify62.0ms (1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series40.0ms (0.6%)

rewrite24.0ms (0.4%)

simplify118.0ms (1.8%)

prune161.0ms (2.5%)

localize12.0ms (0.2%)

series756.0ms (11.8%)

rewrite30.0ms (0.5%)

simplify109.0ms (1.7%)

prune171.0ms (2.7%)

localize13.0ms (0.2%)

series1.1s (17.5%)

rewrite36.0ms (0.6%)

simplify180.0ms (2.8%)

prune411.0ms (6.4%)

localize8.0ms (0.1%)

series37.0ms (0.6%)

rewrite28.0ms (0.4%)

simplify113.0ms (1.8%)

prune182.0ms (2.8%)

regimes894.0ms (13.9%)

simplify4.0ms (0.1%)

end96.0ms (1.5%)

Profiling