Details

analyze630.0ms (11.2%)

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
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	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 14 to 9 computations (35.7% saved)

sample1.1s (19.4%)

Symmetry

(sort y t)

Results

958.0ms	8256×	body	128	valid
51.0ms	415×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

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

5.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	5.7b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	5.7b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series135.0ms (2.4%)

Counts

2 → 84

Calls

2 calls:

123.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
12.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite25.0ms (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:

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

simplify123.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune181.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

Counts

194 → 9

Alt Table

Status	Error	Program
	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	5.7b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
	42.1b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
	3.1b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	20.7b	(.f64 (sqrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))))
	31.6b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))
	3.0b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
▶	2.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	5.7b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))

Compiler

Compiled 5786 to 2145 computations (62.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

series284.0ms (5%)

Counts

4 → 108

Calls

4 calls:

131.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
77.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
39.0ms	(cbrt.f64 x)
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
42×	`associate-r_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 163

Calls

4 calls:

19.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
5.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
1.0ms	(cbrt.f64 x)

simplify123.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
678×	`associate-/l*_binary64`
491×	`associate-/r*_binary64`
190×	`fma-def_binary64`
138×	`*-commutative_binary64`

Counts

271 → 313

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	494	7735
1	1554	6690
2	5178	6690

prune256.0ms (4.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	347	9	356

Error

Counts

356 → 9

Alt Table

Status	Error	Program
▶	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	5.7b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
	42.1b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
	3.1b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	20.7b	(.f64 (sqrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))))
	31.6b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))
	3.0b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	5.7b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))

Compiler

Compiled 9955 to 3006 computations (69.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	2.6b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

series138.0ms (2.4%)

Counts

3 → 96

Calls

3 calls:

113.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
16.0ms	(/.f64 x (-.f64 t z))
8.0ms	(/.f64 1 (-.f64 y z))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

15.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
4.0ms	(/.f64 1 (-.f64 y z))
3.0ms	(/.f64 x (-.f64 t z))

simplify108.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
570×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
186×	`associate-*l/_binary64`
181×	`associate-*r/_binary64`

Counts

252 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6865
1	1402	6443
2	5057	6443

prune285.0ms (5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	278	9	287

Error

Counts

287 → 9

Alt Table

Status	Error	Program
✓	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	5.7b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
	42.1b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
	3.1b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	20.7b	(.f64 (sqrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))))
	31.6b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))
▶	3.0b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.7b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	5.7b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))

Compiler

Compiled 7489 to 2945 computations (60.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.5b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

series147.0ms (2.6%)

Counts

2 → 96

Calls

2 calls:

112.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
34.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

rewrite159.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

1245×	`times-frac_binary64`
825×	`*-un-lft-identity_binary64`
825×	`add-sqr-sqrt_binary64`
457×	`add-cube-cbrt_binary64`
184×	`distribute-lft-out--_binary64`

Counts

2 → 621

Calls

2 calls:

22.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
12.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

simplify397.0ms (7%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-/r/_binary64`
654×	`times-frac_binary64`
231×	`associate-/l/_binary64`
167×	`fma-def_binary64`
144×	`distribute-rgt-in_binary64`

Counts

717 → 720

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	23791
1	1959	23320
2	5004	23320

prune517.0ms (9.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	776	1	777
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	778	8	786

Error

Counts

786 → 8

Alt Table

Status	Error	Program
✓	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	5.7b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
	42.1b	(/.f64 x (.f64 (sqrt.f64 (-.f64 y z)) (.f64 (sqrt.f64 (-.f64 y z)) (-.f64 t z))))
	3.1b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	20.7b	(.f64 (sqrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z)))) (sqrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))))
	31.6b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))
✓	3.0b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	3.4b	(/.f64 (/.f64 1 (/.f64 (-.f64 y z) x)) (-.f64 t z))

Compiler

Compiled 21987 to 6119 computations (72.2% saved)

regimes756.0ms (13.4%)

Accuracy

Total 0.7b remaining (97.7%)

Threshold costs 0.7b (97.7%)

Counts

80 → 3

Compiler

Compiled 8437 to 5111 computations (39.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	69
1	26	69
2	31	69
3	33	69
4	34	69
5	33	69

end99.0ms (1.7%)

Remove: (sort y t)
Compiler: Compiled 336 to 140 computations (58.3% saved)

Details

analyze630.0ms (11.2%)

sample1.1s (19.4%)

simplify75.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series135.0ms (2.4%)

rewrite25.0ms (0.4%)

simplify123.0ms (2.2%)

prune181.0ms (3.2%)

localize11.0ms (0.2%)

series284.0ms (5%)

rewrite45.0ms (0.8%)

simplify123.0ms (2.2%)

prune256.0ms (4.5%)

localize7.0ms (0.1%)

series138.0ms (2.4%)

rewrite34.0ms (0.6%)

simplify108.0ms (1.9%)

prune285.0ms (5%)

localize7.0ms (0.1%)

series147.0ms (2.6%)

rewrite159.0ms (2.8%)

simplify397.0ms (7%)

prune517.0ms (9.1%)

regimes756.0ms (13.4%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end99.0ms (1.7%)

Profiling