Details

analyze322.0ms (6.9%)

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
37.4%	62.4%	0.2%	5
37.4%	62.4%	0.2%	6
43.7%	56.1%	0.2%	7
43.7%	56.1%	0.2%	8
51.5%	48.3%	0.2%	9
51.5%	48.3%	0.2%	10
56.9%	42.9%	0.2%	11
62%	37.8%	0.2%	12
70.4%	29.4%	0.2%	13
70.4%	29.4%	0.2%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample852.0ms (18.3%)

Infinites

4.4% of outputs are infinite.

Symmetry

(sort z t)

Results

667.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify13.0ms (0.3%)

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

prune6.0ms (0.1%)

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

2.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))

series35.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

35.0ms

(/.f64 x (-.f64 y (*.f64 z t)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

3.0ms

(/.f64 x (-.f64 y (*.f64 z t)))

simplify50.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

953×	`times-frac_binary64`
683×	`associate-/l*_binary64`
472×	`associate-/r*_binary64`
302×	`fma-def_binary64`
170×	`associate-/l/_binary64`

Counts

79 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	1915
1	289	1833
2	1061	1688
3	5098	1688

prune50.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Error

2.4b

Counts

73 → 7

Alt Table

Status	Error	Program
	30.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	24.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	25.7b	(.f64 (/.f64 x (.f64 (-.f64 y (.f64 t z)) (fma.f64 t z y))) (+.f64 y (.f64 z t)))
▶	2.6b	(.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)))))
	3.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 y (.f64 z t))) (cbrt.f64 (-.f64 y (.f64 z t))))) (/.f64 x (cbrt.f64 (-.f64 y (*.f64 z t)))))
✓	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 1483 to 476 computations (67.9% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	2.5b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))

series59.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
23.0ms	(/.f64 1 (-.f64 y (*.f64 z t)))

rewrite14.0ms (0.3%)

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)))

simplify116.0ms (2.5%)

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

prune116.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	145	7	152

Error

2.4b

Counts

152 → 7

Alt Table

Status	Error	Program
▶	3.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
	30.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
	24.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	27.0b	(.f64 (.f64 x (/.f64 1 (-.f64 (.f64 y y) (.f64 (.f64 z t) (.f64 z t))))) (+.f64 y (*.f64 z t)))
✓	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	32.1b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))

Compiler

Compiled 2906 to 1183 computations (59.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 1 (-.f64 y (*.f64 z t)))
✓	0.5b	(.f64 (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))))
✓	0.7b	(.f64 x (.f64 (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))))
✓	6.8b	(cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t))))

series841.0ms (18.1%)

Counts

3 → 120

Calls

3 calls:

699.0ms

(*.f64 x (*.f64 (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t))))))

84.0ms

(*.f64 (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))))

59.0ms

(cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t))))

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`cbrt-prod_binary64`
84×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`

Counts

3 → 145

Calls

3 calls:

16.0ms

(*.f64 (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))))

10.0ms

(*.f64 x (*.f64 (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t))))))

3.0ms

(cbrt.f64 (/.f64 1 (-.f64 y (*.f64 z t))))

simplify175.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

672×	`times-frac_binary64`
613×	`associate-l_binary64`
443×	`associate-/r*_binary64`
425×	`fma-def_binary64`
344×	`associate-/l*_binary64`

Counts

265 → 361

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	551	11381
1	1694	10950
2	5030	10950

prune719.0ms (15.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	719	0	719
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	719	7	726

Error

2.4b

Counts

726 → 7

Alt Table

Status	Error	Program
✓	3.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
	30.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
▶	24.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	27.0b	(.f64 (.f64 x (/.f64 1 (-.f64 (.f64 y y) (.f64 (.f64 z t) (.f64 z t))))) (+.f64 y (*.f64 z t)))
✓	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	32.1b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))

Compiler

Compiled 32009 to 16748 computations (47.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))
✓	13.6b	(sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t))))

series164.0ms (3.5%)

Counts

2 → 52

Calls

2 calls:

111.0ms	(sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t))))
53.0ms	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))

rewrite36.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
89×	`sqrt-prod_binary64`
58×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`

Counts

2 → 130

Calls

2 calls:

14.0ms	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
7.0ms	(sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t))))

simplify113.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
324×	`unswap-sqr_binary64`
287×	`associate-r_binary64`
252×	`associate-l_binary64`
228×	`times-frac_binary64`

Counts

182 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	4854
1	656	4563
2	3073	4420
3	5005	4420

prune268.0ms (5.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	433	0	433
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	433	7	440

Error

2.4b

Counts

440 → 7

Alt Table

Status	Error	Program
✓	3.4b	(.f64 (.f64 x (.f64 (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))) (cbrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))
	30.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 y (*.f64 z t)) (sqrt.f64 x)))
✓	24.6b	(.f64 (sqrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (sqrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
✓	2.6b	(.f64 x (/.f64 1 (-.f64 y (.f64 z t))))
	27.0b	(.f64 (.f64 x (/.f64 1 (-.f64 (.f64 y y) (.f64 (.f64 z t) (.f64 z t))))) (+.f64 y (*.f64 z t)))
✓	2.5b	(/.f64 x (-.f64 y (*.f64 z t)))
	32.1b	(.f64 (.f64 x (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t))))) (sqrt.f64 (/.f64 1 (-.f64 y (.f64 z t)))))

Compiler

Compiled 12537 to 2565 computations (79.5% saved)

regimes520.0ms (11.2%)

Accuracy

Total 0.1b remaining (2.1%)

Threshold costs 0.1b (2.1%)

Counts

72 → 1

Compiler

Compiled 11378 to 6543 computations (42.5% 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

end95.0ms (2%)

Remove: (sort z t)
Compiler: Compiled 184 to 107 computations (41.8% 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

analyze322.0ms (6.9%)

sample852.0ms (18.3%)

simplify13.0ms (0.3%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series35.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify50.0ms (1.1%)

prune50.0ms (1.1%)

localize12.0ms (0.3%)

series59.0ms (1.3%)

rewrite14.0ms (0.3%)

simplify116.0ms (2.5%)

prune116.0ms (2.5%)

localize10.0ms (0.2%)

series841.0ms (18.1%)

rewrite48.0ms (1%)

simplify175.0ms (3.8%)

prune719.0ms (15.5%)

localize7.0ms (0.1%)

series164.0ms (3.5%)

rewrite36.0ms (0.8%)

simplify113.0ms (2.4%)

prune268.0ms (5.8%)

regimes520.0ms (11.2%)

simplify3.0ms (0.1%)

end95.0ms (2%)

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