Details

analyze623.0ms (10.9%)

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
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
12.5%	87.3%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
43.7%	56.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.0s (18.2%)

Symmetry

(sort z t)

Results

924.0ms	8256×	body	128	valid
52.0ms	461×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

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

0.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	7.0b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series101.0ms (1.8%)

Counts

2 → 84

Calls

2 calls:

92.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

9.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
6.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
589×	`associate-/l*_binary64`
505×	`associate-/r*_binary64`
195×	`fma-def_binary64`
134×	`*-commutative_binary64`

Counts

173 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	5989
1	1376	5678
2	5010	5678

prune144.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	4	188

Error

0.0b

Counts

188 → 4

Alt Table

Status	Error	Program
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
▶	0.6b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	1.1b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	14.1b	(-.f64 1 (.f64 (sqrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 y t)))) (sqrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))))

Compiler

Compiled 6381 to 2605 computations (59.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.7b	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
✓	7.0b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))

series135.0ms (2.4%)

Counts

2 → 84

Calls

2 calls:

91.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))
44.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
16×	`associate-/r/_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
13×	`prod-exp_binary64`

Counts

2 → 80

Calls

2 calls:

10.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))
9.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))

simplify114.0ms (2%)

Algorithm

1×	egg-herbie

Rules

822×	`associate-/r*_binary64`
815×	`associate-/l*_binary64`
233×	`fma-def_binary64`
162×	`+-commutative_binary64`
140×	`*-commutative_binary64`

Counts

164 → 210

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	548	8284
1	1900	7920
2	5243	7920

prune268.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	301	1	302
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	302	4	306

Error

0.0b

Counts

306 → 4

Alt Table

Status	Error	Program
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	0.6b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	1.1b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
▶	0.6b	(-.f64 1 (*.f64 x (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t))))

Compiler

Compiled 11104 to 5108 computations (54% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.2b	(/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t))
✓	7.0b	(*.f64 x (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t)))

series141.0ms (2.5%)

Counts

3 → 108

Calls

3 calls:

89.0ms	(*.f64 x (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t)))
42.0ms	(/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t))
9.0ms	(/.f64 1 (-.f64 y z))

rewrite79.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

395×	`times-frac_binary64`
329×	`add-sqr-sqrt_binary64`
318×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
111×	`associate-r_binary64`

Counts

3 → 333

Calls

3 calls:

22.0ms	(*.f64 x (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t)))
11.0ms	(/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t))
4.0ms	(/.f64 1 (-.f64 y z))

simplify288.0ms (5%)

Algorithm

1×	egg-herbie

Rules

888×	`associate-/l*_binary64`
834×	`associate-/r*_binary64`
241×	`fma-def_binary64`
174×	`+-commutative_binary64`
156×	`*-commutative_binary64`

Counts

441 → 468

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	683	14421
1	2252	13962
2	5887	13962

prune433.0ms (7.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	467	1	468
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	467	5	472

Error

Counts

472 → 5

Alt Table

Status	Error	Program
▶	0.7b	(-.f64 1 (.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 y t)))))
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	0.6b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	1.1b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
✓	0.6b	(-.f64 1 (*.f64 x (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t))))

Compiler

Compiled 16026 to 7355 computations (54.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
✓	0.5b	(cbrt.f64 (-.f64 y t))
✓	3.1b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 y t))))

series191.0ms (3.3%)

Counts

4 → 120

Calls

4 calls:

108.0ms	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 y t))))
30.0ms	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))
29.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
24.0ms	(cbrt.f64 (-.f64 y t))

rewrite124.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

291×	`times-frac_binary64`
238×	`add-sqr-sqrt_binary64`
236×	`*-un-lft-identity_binary64`
197×	`add-exp-log_binary64`
182×	`associate-r_binary64`

Counts

4 → 364

Calls

4 calls:

35.0ms	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 y t))))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
8.0ms	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))
4.0ms	(cbrt.f64 (-.f64 y t))

simplify265.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

771×	`associate-/l*_binary64`
365×	`fma-def_binary64`
251×	`*-commutative_binary64`
144×	`associate-/l/_binary64`
130×	`+-commutative_binary64`

Counts

484 → 575

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	813	17230
1	2482	15766
2	5168	15766

prune760.0ms (13.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	675	0	675
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	675	5	680

Error

Counts

680 → 5

Alt Table

Status	Error	Program
✓	0.7b	(-.f64 1 (.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 y t)))))
	1.3b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	0.6b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	1.1b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
✓	0.6b	(-.f64 1 (*.f64 x (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 y t))))

Compiler

Compiled 28439 to 12097 computations (57.5% saved)

regimes497.0ms (8.7%)

Accuracy

Total 0.7b remaining (98.2%)

Threshold costs 0.7b (98.2%)

Counts

57 → 1

Compiler

Compiled 8815 to 5582 computations (36.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	24	37
2	36	37
3	50	37
4	61	37
5	70	37
6	74	37
7	75	37
8	73	37

end215.0ms (3.8%)

Compiler: Compiled 208 to 123 computations (40.9% saved)

Details

analyze623.0ms (10.9%)

sample1.0s (18.2%)

simplify117.0ms (2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series101.0ms (1.8%)

rewrite21.0ms (0.4%)

simplify97.0ms (1.7%)

prune144.0ms (2.5%)

localize8.0ms (0.1%)

series135.0ms (2.4%)

rewrite24.0ms (0.4%)

simplify114.0ms (2%)

prune268.0ms (4.7%)

localize8.0ms (0.1%)

series141.0ms (2.5%)

rewrite79.0ms (1.4%)

simplify288.0ms (5%)

prune433.0ms (7.6%)

localize14.0ms (0.2%)

series191.0ms (3.3%)

rewrite124.0ms (2.2%)

simplify265.0ms (4.6%)

prune760.0ms (13.3%)

regimes497.0ms (8.7%)

simplify3.0ms (0.1%)

end215.0ms (3.8%)

Profiling