Details

analyze996.0ms (30.6%)

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
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.2s (35.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify26.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
471×	`div-sub_binary64`
457×	`associate-*l/_binary64`
448×	`cancel-sign-sub-inv_binary64`
340×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	25
2	76	25
3	193	22
4	558	19
5	1508	19
6	3813	19

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
	11.3b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 74 computations (32.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
✓	0.0b	(*.f64 2 (/.f64 z y))
✓	0.0b	(-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))
✓	0.8b	(/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))

series79.0ms (2.4%)

Counts

4 → 93

Calls

4 calls:

38.0ms	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
21.0ms	(/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))
13.0ms	(-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))
6.0ms	(*.f64 2 (/.f64 z y))

rewrite69.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`expm1-udef_binary64`
275×	`log1p-udef_binary64`
152×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	299	55
2	4311	55

Stop Event

1×	node limit

Counts

4 → 125

Calls

4 calls:

65.0ms	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
65.0ms	(*.f64 2 (/.f64 z y))
65.0ms	(-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))
65.0ms	(/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z)))

simplify62.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-neg_binary64`
529×	`times-frac_binary64`
334×	`associate-/l*_binary64`
293×	`associate-/r*_binary64`
239×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	94	2292
1	285	2282
2	889	2282
3	4721	2282

Stop Event

1×	node limit

Counts

218 → 166

prune119.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	163	5	168

Error

0.0b

Counts

168 → 5

Alt Table

Status	Error	Program
	23.4b	(+.f64 x (/.f64 -2 (*.f64 2 (/.f64 z y))))
▶	7.2b	(+.f64 x (/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))))
✓	0.1b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
	23.3b	(-.f64 x (/.f64 y z))
	24.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 3730 to 1961 computations (47.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z))
✓	0.2b	(pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3)
✓	0.8b	(/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3)))
✓	27.2b	(cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))

series77.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

27.0ms	(/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3)))
22.0ms	(pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3)
14.0ms	(cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))
13.0ms	(fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z))

rewrite106.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

355×	`egg-rr`
228×	`prod-diff_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	301	50
2	3696	50

Stop Event

1×	node limit

Counts

4 → 355

Calls

4 calls:

96.0ms	(fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z))
96.0ms	(pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3)
96.0ms	(/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3)))
96.0ms	(cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

681×	`times-frac_binary64`
462×	`associate-/l*_binary64`
370×	`associate-/r*_binary64`
280×	`associate-r_binary64`
251×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	3169
1	259	3145
2	959	3116

Stop Event

1×	node limit

Counts

499 → 250

prune187.0ms (5.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	250	5	255

Error

0.0b

Counts

255 → 5

Alt Table

Status	Error	Program
	23.4b	(+.f64 x (/.f64 -2 (*.f64 2 (/.f64 z y))))
✓	7.2b	(+.f64 x (/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))))
✓	0.1b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
▶	23.3b	(-.f64 x (/.f64 y z))
	24.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 8032 to 4012 computations (50% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

0.0b

Counts

5 → 5

Alt Table

Status	Error	Program
▶	23.4b	(+.f64 x (/.f64 -2 (*.f64 2 (/.f64 z y))))
✓	7.2b	(+.f64 x (/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))))
✓	0.1b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
✓	23.3b	(-.f64 x (/.f64 y z))
	24.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 92 to 67 computations (27.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 2 (/.f64 z y))
✓	0.8b	(/.f64 -2 (*.f64 2 (/.f64 z y)))

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(/.f64 -2 (*.f64 2 (/.f64 z y)))

rewrite39.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

812×	`log1p-expm1-u_binary64`
812×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	176	7
2	2223	7

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

39.0ms

(/.f64 -2 (*.f64 2 (/.f64 z y)))

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
8×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-neg_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	144
1	10	144
2	17	144
3	23	144
4	29	144
5	37	144
6	45	144
7	55	144
8	63	144
9	77	144

Stop Event

1×

saturated

Counts

50 → 27

prune28.0ms (0.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	49	5	54

Error

0.0b

Counts

54 → 5

Alt Table

Status	Error	Program
✓	23.4b	(+.f64 x (/.f64 -2 (*.f64 2 (/.f64 z y))))
✓	7.2b	(+.f64 x (/.f64 -2 (cbrt.f64 (pow.f64 (fma.f64 2 (/.f64 z y) (/.f64 (neg.f64 t) z)) 3))))
✓	0.1b	(+.f64 x (/.f64 -2 (-.f64 (*.f64 2 (/.f64 z y)) (/.f64 t z))))
✓	23.3b	(-.f64 x (/.f64 y z))
	24.4b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 601 to 377 computations (37.3% saved)

regimes114.0ms (3.5%)

Accuracy

Total 0.1b remaining (89.7%)

Threshold costs 0.1b (89.7%)

Counts

17 → 1

Compiler

Compiled 1798 to 1246 computations (30.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	17	19
2	24	19
3	28	19
4	31	19
5	32	19

Stop Event

1×

saturated

end69.0ms (2.1%)

Compiler: Compiled 103 to 74 computations (28.2% saved)

Details

analyze996.0ms (30.6%)

sample1.2s (35.7%)

simplify26.0ms (0.8%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series79.0ms (2.4%)

rewrite69.0ms (2.1%)

simplify62.0ms (1.9%)

prune119.0ms (3.7%)

localize15.0ms (0.5%)

series77.0ms (2.4%)

rewrite106.0ms (3.3%)

simplify61.0ms (1.9%)

prune187.0ms (5.8%)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series6.0ms (0.2%)

rewrite39.0ms (1.2%)

simplify14.0ms (0.4%)

prune28.0ms (0.9%)

regimes114.0ms (3.5%)

simplify2.0ms (0.1%)

end69.0ms (2.1%)

Profiling