Details

analyze575.0ms (11.6%)

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
0%	99.8%	0.2%	6
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (22.7%)

Symmetry

(sort z t)

Results

921.0ms	8256×	body	128	valid
40.0ms	362×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

3.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.7b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	3.7b	(/.f64 x (-.f64 y (*.f64 z t)))

series43.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

38.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.f64 y (*.f64 z t))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

4.0ms	(-.f64 y (*.f64 z t))
3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

761×	`associate-/l*_binary64`
527×	`associate-/r*_binary64`
388×	`fma-def_binary64`
188×	`fma-neg_binary64`
173×	`associate-*l/_binary64`

Counts

135 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2389
1	332	2275
2	1159	2114
3	4821	2114
4	4954	2114

prune86.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	9	111

Error

3.6b

Counts

111 → 9

Alt Table

Status	Error	Program
	38.6b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	4.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y (.f64 z t)))))
✓	3.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	29.9b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
	4.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	27.7b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
▶	3.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	33.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
	29.9b	(/.f64 x y)

Compiler

Compiled 2023 to 623 computations (69.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.3b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	3.4b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series62.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
25.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite18.0ms (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 → 75

Calls

2 calls:

10.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify106.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-/r*_binary64`
540×	`fma-def_binary64`
347×	`associate-*l/_binary64`
222×	`fma-neg_binary64`
200×	`associate-/l/_binary64`

Counts

159 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	3528
1	394	3335
2	1569	3102
3	4897	3102
4	5060	3102

prune146.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	183	9	192

Error

3.6b

Counts

192 → 9

Alt Table

Status	Error	Program
	38.6b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	4.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y (.f64 z t)))))
	30.0b	(*.f64 x (/.f64 1 y))
	33.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
✓	3.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	29.9b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
▶	4.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	27.7b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
✓	3.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 3508 to 1391 computations (60.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.9b	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
✓	2.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))

series369.0ms (7.4%)

Counts

4 → 120

Calls

4 calls:

233.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
52.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
51.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

12.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
4.0ms	(/.f64 (-.f64 y (*.f64 z t)) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify195.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
412×	`unswap-sqr_binary64`
344×	`associate-/l*_binary64`
220×	`div-sub_binary64`
183×	`times-frac_binary64`

Counts

285 → 293

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	254	5914
1	620	5095
2	2919	4957
3	4021	4873
4	4838	4873
5	4976	4873

prune199.0ms (4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	329	9	338

Error

3.6b

Counts

338 → 9

Alt Table

Status	Error	Program
	38.6b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
▶	4.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y (.f64 z t)))))
	30.0b	(*.f64 x (/.f64 1 y))
	33.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
✓	3.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	29.9b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
✓	4.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	27.7b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
✓	3.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 7387 to 1580 computations (78.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
✓	0.8b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))))
✓	7.4b	(cbrt.f64 (-.f64 y (*.f64 z t)))

series715.0ms (14.4%)

Counts

2 → 84

Calls

2 calls:

659.0ms	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t)))))
56.0ms	(cbrt.f64 (-.f64 y (*.f64 z t)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`cbrt-div_binary64`
14×	`add-exp-log_binary64`
8×	`associate-/r/_binary64`
7×	`flip--_binary64`
7×	`flip3--_binary64`

Counts

2 → 46

Calls

2 calls:

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

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

581×	`times-frac_binary64`
450×	`associate-/r*_binary64`
357×	`associate-/l*_binary64`
310×	`associate-l_binary64`
252×	`fma-def_binary64`

Counts

130 → 199

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	474	6509
1	1510	5946
2	5296	5946

prune364.0ms (7.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	472	0	472
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	472	9	481

Error

3.6b

Counts

481 → 9

Alt Table

Status	Error	Program
	38.6b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
✓	4.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y (.f64 z t)))))
	30.0b	(*.f64 x (/.f64 1 y))
	33.6b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 y (.f64 z t)))) (/.f64 x (sqrt.f64 (-.f64 y (*.f64 z t)))))
✓	3.7b	(/.f64 x (-.f64 y (*.f64 z t)))
	29.9b	(/.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 y (.f64 z t)) (-.f64 y (.f64 z t))) (-.f64 y (*.f64 z t)))))
✓	4.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (-.f64 y (.f64 z t)) (cbrt.f64 x)))
	27.7b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
✓	3.8b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

Compiler

Compiled 22923 to 7798 computations (66% saved)

regimes533.0ms (10.7%)

Accuracy

Total 0.1b remaining (2.3%)

Threshold costs 0.1b (2.3%)

Counts

74 → 1

Compiler

Compiled 10650 to 5892 computations (44.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	30	10
4	34	10
5	35	10
6	35	10

end102.0ms (2.1%)

Remove: (sort z t)
Compiler: Compiled 210 to 116 computations (44.8% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Details

analyze575.0ms (11.6%)

sample1.1s (22.7%)

simplify18.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series43.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify86.0ms (1.7%)

prune86.0ms (1.7%)

localize6.0ms (0.1%)

series62.0ms (1.2%)

rewrite18.0ms (0.4%)

simplify106.0ms (2.1%)

prune146.0ms (2.9%)

localize9.0ms (0.2%)

series369.0ms (7.4%)

rewrite36.0ms (0.7%)

simplify195.0ms (3.9%)

prune199.0ms (4%)

localize12.0ms (0.2%)

series715.0ms (14.4%)

rewrite16.0ms (0.3%)

simplify112.0ms (2.3%)

prune364.0ms (7.3%)

regimes533.0ms (10.7%)

simplify2.0ms (0%)

end102.0ms (2.1%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10