Details

analyze1.7s (26.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.6s (24.8%)

Results

1.2s	8252×	body	128	valid
242.0ms	361×	body	8192	exit
68.0ms	397×	body	128	invalid
1.0ms	2×	body	512	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

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

1.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 58 to 31 computations (46.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	2.0b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series108.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

48.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
35.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
25.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 122

Calls

3 calls:

10.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
6.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
2.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
498×	`sub-neg_binary64`
213×	`associate--l+_binary64`
201×	`fma-neg_binary64`
200×	`+-commutative_binary64`

Counts

266 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	6584
1	983	6188
2	3712	6122
3	5248	6122

prune177.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	238	4	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Error

Counts

243 → 5

Alt Table

Status	Error	Program
▶	2.9b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))))
	29.8b	(+.f64 x (.f64 (sqrt.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	9.7b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
	9.7b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 6329 to 1885 computations (70.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
✓	0.6b	(cbrt.f64 (-.f64 z a))
✓	7.7b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))

series246.0ms (3.9%)

Counts

4 → 132

Calls

4 calls:

135.0ms	(/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))
40.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
38.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
32.0ms	(cbrt.f64 (-.f64 z a))

rewrite76.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
127×	`*-un-lft-identity_binary64`
90×	`times-frac_binary64`
90×	`cbrt-prod_binary64`
55×	`add-cube-cbrt_binary64`

Counts

4 → 240

Calls

4 calls:

26.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
9.0ms	(/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))
9.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
2.0ms	(cbrt.f64 (-.f64 z a))

simplify256.0ms (4%)

Algorithm

1×	egg-herbie

Rules

332×	`fma-def_binary64`
311×	`times-frac_binary64`
293×	`associate-/l*_binary64`
272×	`associate-/r*_binary64`
207×	`associate-*l/_binary64`

Counts

372 → 407

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	664	11687
1	1968	10769
2	4973	10769
3	4956	10769

prune400.0ms (6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	507	0	507
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	507	5	512

Error

Counts

512 → 5

Alt Table

Status	Error	Program
✓	2.9b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))))
	29.8b	(+.f64 x (.f64 (sqrt.f64 (.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))) (sqrt.f64 (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
	9.7b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 z a))))
▶	9.7b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 19481 to 6960 computations (64.3% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	9.7b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))

series87.0ms (1.4%)

Counts

3 → 120

Calls

3 calls:

47.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
33.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
7.0ms	(*.f64 (-.f64 z t) y)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

7.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a))
6.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
4.0ms	(*.f64 (-.f64 z t) y)

simplify130.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
563×	`cancel-sign-sub-inv_binary64`
333×	`sub-neg_binary64`
196×	`div-sub_binary64`
166×	`fma-neg_binary64`

Counts

192 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	258	4561
1	727	4147
2	2695	3786
3	4896	3783
4	4975	3783

prune122.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	0	2
Picked	0	1	1
Done	0	2	2
Total	188	5	193

Error

Counts

193 → 5

Alt Table

Status	Error	Program
✓	2.9b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))))
▶	3.2b	(+.f64 x (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))))
✓	9.7b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))
	10.1b	(+.f64 x (/.f64 (.f64 (.f64 (-.f64 z t) (*.f64 (cbrt.f64 y) (cbrt.f64 y))) (cbrt.f64 y)) (-.f64 z a)))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 4571 to 1352 computations (70.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))))
✓	0.0b	(/.f64 y (-.f64 z a))
✓	9.8b	(*.f64 (-.f64 z t) (/.f64 y (-.f64 z a)))

series104.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

50.0ms	(+.f64 x (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))))
35.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 z a)))
19.0ms	(/.f64 y (-.f64 z a))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 103

Calls

3 calls:

16.0ms	(*.f64 (-.f64 z t) (/.f64 y (-.f64 z a)))
9.0ms	(/.f64 y (-.f64 z a))
3.0ms	(+.f64 x (*.f64 (-.f64 z t) (/.f64 y (-.f64 z a))))

simplify158.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

924×	`times-frac_binary64`
473×	`fma-neg_binary64`
320×	`sub-neg_binary64`
167×	`+-commutative_binary64`
161×	`associate-/l*_binary64`

Counts

235 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	5886
1	838	5268
2	3129	5226
3	4721	5223
4	5012	5223

prune134.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	222	4	226

Error

Counts

226 → 4

Alt Table

Status	Error	Program
✓	2.9b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a)))))
	3.2b	(fma.f64 (-.f64 z t) (/.f64 y (-.f64 z a)) x)
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	9.7b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 z a)))

Compiler

Compiled 5505 to 1606 computations (70.8% saved)

regimes546.0ms (8.6%)

Accuracy

Total 0.6b remaining (96.9%)

Threshold costs 0.6b (96.9%)

Counts

66 → 3

Compiler

Compiled 9768 to 5912 computations (39.5% saved)

bsearch59.0ms (0.9%)

Steps

Iters	Range		Point
8	6.231100338045555e-49	3.3255709838982975e-46	9.715510485428454e-48
10	-1.3458592483860822e+60	-1.6080766068451695e+41	-9.042638636563712e+45

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	30	58
2	38	58
3	42	58
4	44	58
5	44	58

end75.0ms (1.2%)

Compiler: Compiled 164 to 82 computations (50% saved)

Details

analyze1.7s (26.9%)

sample1.6s (24.8%)

simplify116.0ms (1.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series108.0ms (1.7%)

rewrite31.0ms (0.5%)

simplify141.0ms (2.2%)

prune177.0ms (2.8%)

localize12.0ms (0.2%)

series246.0ms (3.9%)

rewrite76.0ms (1.2%)

simplify256.0ms (4%)

prune400.0ms (6.3%)

localize11.0ms (0.2%)

series87.0ms (1.4%)

rewrite20.0ms (0.3%)

simplify130.0ms (2.1%)

prune122.0ms (1.9%)

localize8.0ms (0.1%)

series104.0ms (1.6%)

rewrite34.0ms (0.5%)

simplify158.0ms (2.5%)

prune134.0ms (2.1%)

regimes546.0ms (8.6%)

bsearch59.0ms (0.9%)

simplify4.0ms (0.1%)

end75.0ms (1.2%)

Profiling