Details

analyze1.2s (16%)

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
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample3.6s (46.5%)

Symmetry

(sort y z)

Results

2.0s	10789×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

2067×	`associate-/l*_binary64`
1151×	`associate-/l/_binary64`
961×	`associate-/r/_binary64`
904×	`*-commutative_binary64`
879×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	121	20
3	446	20
4	1750	20
5	3005	20
6	3002	20
7	3002	20
8	3753	20
9	4074	20
10	4215	20
11	4225	20
12	4229	20
13	4230	20
14	5398	20

prune4.0ms (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

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.7b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
▶	1.5b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

Compiler

Compiled 116 to 91 computations (21.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 3 (/.f64 x (.f64 y 27)))
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	2.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	4.3b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series119.0ms (1.6%)

Counts

4 → 144

Calls

4 calls:

56.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
39.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
18.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
6.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-exp-log_binary64`
92×	`add-cbrt-cube_binary64`
41×	`prod-exp_binary64`
39×	`cbrt-unprod_binary64`
31×	`add-sqr-sqrt_binary64`

Counts

4 → 141

Calls

4 calls:

9.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
8.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
6.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
5.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

simplify264.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

782×	`associate-/r/_binary64`
291×	`times-frac_binary64`
262×	`sub-neg_binary64`
198×	`associate-l_binary64`
191×	`log-prod_binary64`

Counts

285 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	5969
1	547	4670
2	2441	4667
3	4043	4667
4	4793	4667
5	4977	4667

prune198.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	211	2	213

Error

0.0b

Counts

213 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
▶	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Status

Error

Program

1.0b

(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))

▶

0.6b

(*.f64 (/.f64 1 (*.f64 (cbrt.f64 3) (cbrt.f64 3))) (*.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (*.f64 (/.f64 (*.f64 3 (/.f64 x (*.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Compiler

Compiled 5848 to 4191 computations (28.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	1.0b	(/.f64 1 (cbrt.f64 3))
	2.0b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
	4.3b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series99.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

99.0ms	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
0.0ms	(/.f64 1 (cbrt.f64 3))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
23×	`cbrt-prod_binary64`

Counts

2 → 94

Calls

2 calls:

6.0ms	(.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
3.0ms	(/.f64 1 (cbrt.f64 3))

simplify218.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

958×	`fabs-mul_binary64`
446×	`unswap-sqr_binary64`
434×	`associate-/l*_binary64`
319×	`associate-/l/_binary64`
314×	`associate-*l/_binary64`

Counts

142 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	97	3282
1	176	2929
2	463	2797
3	974	2775
4	2575	2775
5	2672	2775
6	2888	2775
7	3204	2775
8	4279	2775
9	4834	2775
10	4803	2775
11	5052	2775

prune309.0ms (4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	236	3	239

Error

Counts

239 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Compiler

Compiled 8726 to 6893 computations (21% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))
✓	0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	2.0b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	4.9b	(/.f64 x (*.f64 y z))

series148.0ms (1.9%)

Counts

4 → 0

Calls

4 calls:

58.0ms	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))
39.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
34.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
16.0ms	(/.f64 x (*.f64 y z))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
30×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 123

Calls

4 calls:

8.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
6.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
3.0ms	(/.f64 x (*.f64 y z))
3.0ms	(/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3))

simplify135.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

964×	`times-frac_binary64`
493×	`associate-/l*_binary64`
456×	`associate-/r*_binary64`
315×	`*-commutative_binary64`
192×	`fma-def_binary64`

Counts

123 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	2927
1	375	2612
2	1154	2612
3	3839	2608
4	4789	2608
5	4936	2608
6	4949	2608

prune185.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	168	3	171

Error

Counts

171 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
▶	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Compiler

Compiled 5392 to 3345 computations (38% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
	2.0b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	4.9b	(/.f64 x (*.f64 y z))

series18.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

18.0ms

(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

3.0ms

(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

632×	`associate-l_binary64`
551×	`unswap-sqr_binary64`
231×	`sqr-pow_binary64`
224×	`associate-*r/_binary64`
220×	`associate-*l/_binary64`

Counts

20 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	542
1	79	466
2	153	465
3	267	465
4	411	465
5	596	465
6	810	465
7	1434	465
8	3195	465
9	3845	465
10	4923	465
11	4854	465

prune50.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	118	3	121

Error

Counts

121 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))) (cbrt.f64 3)))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	0.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (.f64 (/.f64 1 (cbrt.f64 3)) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t)))))

Compiler

Compiled 2425 to 1087 computations (55.2% saved)

regimes694.0ms (9.1%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Counts

37 → 1

Compiler

Compiled 15916 to 13301 computations (16.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	27	38
2	26	38

end95.0ms (1.2%)

Remove: (sort y z)
Compiler: Compiled 187 to 159 computations (15% saved)

Details

analyze1.2s (16%)

sample3.6s (46.5%)

simplify91.0ms (1.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series119.0ms (1.6%)

rewrite41.0ms (0.5%)

simplify264.0ms (3.5%)

prune198.0ms (2.6%)

localize19.0ms (0.3%)

series99.0ms (1.3%)

rewrite19.0ms (0.3%)

simplify218.0ms (2.8%)

prune309.0ms (4%)

localize15.0ms (0.2%)

series148.0ms (1.9%)

rewrite27.0ms (0.3%)

simplify135.0ms (1.8%)

prune185.0ms (2.4%)

localize10.0ms (0.1%)

series18.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify88.0ms (1.1%)

prune50.0ms (0.6%)

regimes694.0ms (9.1%)

simplify3.0ms (0%)

end95.0ms (1.2%)

Profiling