Details

analyze701.0ms (7.6%)

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
37.4%	62.3%	0.2%	6
37.4%	62.3%	0.2%	7
37.4%	62.3%	0.2%	8
37.4%	62.3%	0.2%	9
43.6%	56.1%	0.2%	10
51.4%	48.3%	0.2%	11
51.4%	48.3%	0.2%	12
51.4%	48.3%	0.2%	13
55.3%	44.4%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample927.0ms (10%)

Results

834.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify115.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1539×	`fma-neg_binary64`
1346×	`fma-def_binary64`
1046×	`div-sub_binary64`
750×	`associate-/r/_binary64`
420×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune2.0ms (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

10.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	0.0b	(-.f64 t (*.f64 a z))
✓	10.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series85.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

74.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
6.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 74

Calls

3 calls:

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

simplify126.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

886×	`fma-def_binary64`
731×	`cancel-sign-sub-inv_binary64`
207×	`sub-neg_binary64`
192×	`fma-neg_binary64`
173×	`times-frac_binary64`

Counts

152 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	4118
1	671	3825
2	2454	3679
3	4965	3679
4	4935	3679

prune212.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	153	10	163
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	11	164

Error

3.4b

Counts

164 → 11

Alt Table

Status	Error	Program
	33.3b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	11.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	38.5b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 a z)))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))))
✓	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	37.9b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (sqrt.f64 t) (sqrt.f64 t) (neg.f64 (.f64 a z))))
	31.8b	(/.f64 (-.f64 x (*.f64 y z)) t)
	39.8b	(/.f64 y a)
	33.5b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
▶	10.6b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	10.6b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	38.2b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))

Compiler

Compiled 4331 to 1271 computations (70.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
	0.0b	(-.f64 t (*.f64 a z))
✓	0.3b	(/.f64 1 (-.f64 t (*.f64 a z)))
✓	10.3b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))

series176.0ms (1.9%)

Counts

2 → 96

Calls

2 calls:

135.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
41.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 79

Calls

2 calls:

19.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
7.0ms	(/.f64 1 (-.f64 t (*.f64 a z)))

simplify289.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

717×	`cancel-sign-sub-inv_binary64`
335×	`fma-neg_binary64`
295×	`distribute-rgt-in_binary64`
210×	`times-frac_binary64`
205×	`sub-neg_binary64`

Counts

175 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5382
1	682	4890
2	2696	4652
3	4643	4651
4	4987	4651

prune425.0ms (4.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	240	11	251

Error

2.2b

Counts

251 → 11

Alt Table

Status	Error	Program
	33.3b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	11.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	38.5b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 a z)))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))))
✓	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	31.8b	(/.f64 (-.f64 x (*.f64 y z)) t)
	39.8b	(/.f64 y a)
	35.8b	(.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (.f64 (.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 t (.f64 a z)))) (/.f64 1 (-.f64 t (*.f64 a z))))))
	33.3b	(.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (/.f64 1 (-.f64 t (*.f64 a z))))
	33.5b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
▶	10.6b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	35.2b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))

Compiler

Compiled 6263 to 2163 computations (65.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
	0.0b	(-.f64 t (*.f64 a z))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	10.4b	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

series239.0ms (2.6%)

Counts

2 → 120

Calls

2 calls:

130.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))
108.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`

Counts

2 → 120

Calls

2 calls:

14.0ms	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
14.0ms	(/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z)))

simplify434.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

398×	`sub-neg_binary64`
351×	`times-frac_binary64`
310×	`fma-neg_binary64`
262×	`associate-/l*_binary64`
231×	`associate-/r*_binary64`

Counts

240 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	8921
1	1048	8344
2	4130	8272
3	4944	8272
4	4953	8272

prune508.0ms (5.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	324	12	336

Error

2.1b

Counts

336 → 12

Alt Table

Status	Error	Program
	33.3b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
▶	11.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	38.5b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 a z)))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))))
✓	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	31.8b	(/.f64 (-.f64 x (*.f64 y z)) t)
	39.8b	(/.f64 y a)
	35.8b	(.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (.f64 (.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 t (.f64 a z)))) (/.f64 1 (-.f64 t (*.f64 a z))))))
	33.3b	(.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (/.f64 1 (-.f64 t (*.f64 a z))))
	33.5b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	34.4b	(/.f64 1 (-.f64 (fma.f64 (/.f64 a (.f64 y y)) (/.f64 x z) (/.f64 a y)) (/.f64 t (.f64 z y))))
✓	10.6b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	35.2b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))

Compiler

Compiled 9721 to 3046 computations (68.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z))))
✓	3.4b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
✓	4.6b	(/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (.f64 y z))))
✓	9.5b	(cbrt.f64 (-.f64 x (*.f64 y z)))

series911.0ms (9.8%)

Counts

4 → 192

Calls

4 calls:

529.0ms	(/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (.f64 y z))))
155.0ms	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
115.0ms	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z))))
111.0ms	(cbrt.f64 (-.f64 x (*.f64 y z)))

rewrite105.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
49×	`cbrt-prod_binary64`

Counts

4 → 189

Calls

4 calls:

28.0ms	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
14.0ms	(.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (*.f64 y z))))
10.0ms	(/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (.f64 y z))))
4.0ms	(cbrt.f64 (-.f64 x (*.f64 y z)))

simplify535.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

851×	`times-frac_binary64`
540×	`fma-def_binary64`
291×	`*-commutative_binary64`
123×	`+-commutative_binary64`
102×	`sub-neg_binary64`

Counts

381 → 522

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	911	18371
1	2962	17500
2	5030	17500

prune1.2s (12.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	665	1	666
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	665	13	678

Error

2.1b

Counts

678 → 13

Alt Table

Status	Error	Program
	39.8b	(/.f64 y a)
	47.8b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (.f64 t (pow.f64 (/.f64 1 (-.f64 x (*.f64 y z))) 1/3)))
	33.3b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
✓	11.2b	(/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (-.f64 t (.f64 a z)) (cbrt.f64 (-.f64 x (*.f64 y z)))))
	38.5b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 t (.f64 a z)))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))))
✓	10.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
	31.8b	(/.f64 (-.f64 x (*.f64 y z)) t)
	35.8b	(.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (.f64 (.f64 (/.f64 1 (-.f64 t (.f64 a z))) (/.f64 1 (-.f64 t (.f64 a z)))) (/.f64 1 (-.f64 t (*.f64 a z))))))
	33.3b	(.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (/.f64 1 (-.f64 t (*.f64 a z))))
	33.5b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	34.4b	(/.f64 1 (-.f64 (fma.f64 (/.f64 a (.f64 y y)) (/.f64 x z) (/.f64 a y)) (/.f64 t (.f64 z y))))
✓	10.6b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	35.2b	(-.f64 (.f64 (+.f64 (/.f64 (.f64 z a) t) 1) (/.f64 x t)) (.f64 (/.f64 y t) (+.f64 z (/.f64 (.f64 z (*.f64 z a)) t))))

Compiler

Compiled 34240 to 11732 computations (65.7% saved)

regimes1.8s (19.3%)

Accuracy

Total 5.3b remaining (73.7%)

Threshold costs 0b (0%)

Counts

113 → 2

Compiler

Compiled 16532 to 9246 computations (44.1% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	41
1	28	41
2	45	41
3	55	41
4	61	41
5	62	41
6	62	41

end329.0ms (3.6%)

Compiler: Compiled 364 to 200 computations (45.1% saved)

Details

analyze701.0ms (7.6%)

sample927.0ms (10%)

simplify115.0ms (1.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series85.0ms (0.9%)

rewrite18.0ms (0.2%)

simplify126.0ms (1.4%)

prune212.0ms (2.3%)

localize18.0ms (0.2%)

series176.0ms (1.9%)

rewrite37.0ms (0.4%)

simplify289.0ms (3.1%)

prune425.0ms (4.6%)

localize19.0ms (0.2%)

series239.0ms (2.6%)

rewrite55.0ms (0.6%)

simplify434.0ms (4.7%)

prune508.0ms (5.5%)

localize21.0ms (0.2%)

series911.0ms (9.8%)

rewrite105.0ms (1.1%)

simplify535.0ms (5.8%)

prune1.2s (12.6%)

regimes1.8s (19.3%)

bsearch8.0ms (0.1%)

simplify6.0ms (0.1%)

end329.0ms (3.6%)

Profiling