Details

analyze482.0ms (15%)

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)

sample134.0ms (4.2%)

Algorithm

1×

intervals

Symmetry

(sort z t)

Results

8.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify12.0ms (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

prune1.0ms (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

2.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))

series42.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.f64 y (*.f64 z t))

rewrite7.0ms (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:

3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
2.0ms	(-.f64 y (*.f64 z t))

simplify94.0ms (2.9%)

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

prune77.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	6	111

Error

2.8b

Counts

111 → 6

Alt Table

Status	Error	Program
▶	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	4.0b	(.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)))))
	23.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))

Compiler

Compiled 1937 to 565 computations (70.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.2b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series61.0ms (1.9%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
23.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite14.0ms (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:

7.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
3.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

simplify104.0ms (3.2%)

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

prune133.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	183	6	189

Error

2.8b

Counts

189 → 6

Alt Table

Status	Error	Program
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
▶	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	3.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))

Compiler

Compiled 3392 to 1327 computations (60.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.9b	(/.f64 (-.f64 y (*.f64 z t)) x)

series53.0ms (1.7%)

Counts

2 → 96

Calls

2 calls:

34.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
19.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 110

Calls

2 calls:

5.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
3.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify119.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/l*_binary64`
526×	`associate-/r*_binary64`
409×	`fma-def_binary64`
329×	`associate-/r/_binary64`
251×	`associate-/l/_binary64`

Counts

206 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	4158
1	402	3845
2	1455	3696
3	4932	3696
4	5008	3696

prune150.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	225	7	232

Error

2.8b

Counts

232 → 7

Alt Table

Status	Error	Program
▶	3.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))
	3.8b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 (cbrt.f64 (-.f64 y (.f64 z t))) x))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))

Compiler

Compiled 4344 to 1371 computations (68.4% saved)

localize9.0ms (0.3%)

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)
✓	1.2b	(.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t))))
✓	2.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))

series223.0ms (6.9%)

Counts

4 → 120

Calls

4 calls:

104.0ms	(.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t))))
45.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))
37.0ms	(cbrt.f64 x)
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
44×	`add-sqr-sqrt_binary64`
28×	`prod-exp_binary64`
25×	`cbrt-prod_binary64`
25×	`pow1_binary64`

Counts

4 → 135

Calls

4 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))
7.0ms	(.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t))))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify199.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

529×	`unswap-sqr_binary64`
343×	`associate-l_binary64`
295×	`associate-r_binary64`
265×	`fma-neg_binary64`
250×	`cancel-sign-sub-inv_binary64`

Counts

255 → 228

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	230	4996
1	581	4418
2	2741	4361
3	4167	4346
4	4825	4346
5	4995	4346
6	4954	4346

prune158.0ms (4.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	264	0	264
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	264	7	271

Error

2.8b

Counts

271 → 7

Alt Table

Status	Error	Program
✓	3.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (/.f64 1 (-.f64 y (.f64 z t)))))
	3.8b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 t z))) (cbrt.f64 (-.f64 y (.f64 t z))))) (/.f64 (cbrt.f64 (-.f64 y (.f64 z t))) x))
✓	3.0b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
✓	3.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	2.9b	(/.f64 x (-.f64 y (*.f64 z t)))
	23.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	3.8b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))

Compiler

Compiled 6117 to 2025 computations (66.9% saved)

regimes414.0ms (12.9%)

Accuracy

Total 0.1b remaining (2.1%)

Threshold costs 0.1b (2.1%)

Counts

65 → 1

Compiler

Compiled 8662 to 5115 computations (40.9% saved)

simplify3.0ms (0.1%)

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

end5.0ms (0.1%)

Remove: (sort z t)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample658.0ms (20.4%)

Algorithm

1×

intervals

Results

304.0ms	8000×	body	128	valid
11.0ms	339×	body	128	invalid

Compiler

Compiled 163 to 90 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

analyze482.0ms (15%)

sample134.0ms (4.2%)

simplify12.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series42.0ms (1.3%)

rewrite7.0ms (0.2%)

simplify94.0ms (2.9%)

prune77.0ms (2.4%)

localize9.0ms (0.3%)

series61.0ms (1.9%)

rewrite14.0ms (0.4%)

simplify104.0ms (3.2%)

prune133.0ms (4.1%)

localize6.0ms (0.2%)

series53.0ms (1.7%)

rewrite16.0ms (0.5%)

simplify119.0ms (3.7%)

prune150.0ms (4.6%)

localize9.0ms (0.3%)

series223.0ms (6.9%)

rewrite35.0ms (1.1%)

simplify199.0ms (6.2%)

prune158.0ms (4.9%)

regimes414.0ms (12.9%)

simplify3.0ms (0.1%)

end5.0ms (0.1%)

sample658.0ms (20.4%)

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