Details

analyze1.4s (13.6%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (13.1%)

Alt Table

Status	Error	Program
▶	9.7b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Results

1.1s	8256×	body	128	valid
123.0ms	753×	body	128	invalid

Compiler

Compiled 82 to 52 computations (36.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 a z))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	9.5b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series75.0ms (0.7%)

Counts

3 → 78

Calls

3 calls:

64.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite125.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

412×	`fma-def_binary64`
244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
217×	`egg-rr`
195×	`fma-neg_binary64`

Counts

3 → 217

Calls

3 calls:

118.0ms	(-.f64 t (*.f64 a z))
118.0ms	(-.f64 x (*.f64 y z))
118.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	253	30
2	3617	30
3	4990	30
4	5001	30
0	0	0
1	0	0

prune247.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	284	11	295
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	285	11	296

Error

2.6b

Counts

296 → 11

Alt Table

Status	Error	Program
▶	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
	32.8b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (-.f64 (.f64 t t) (pow.f64 (.f64 z a) 2)) (/.f64 1 (fma.f64 z a t)) (fma.f64 (neg.f64 a) z (.f64 z a))))
	41.4b	(/.f64 y a)
	34.0b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 2) (-.f64 t (.f64 a z)))
	10.5b	(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 t (.f64 z a))) 2)) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 z a)))))
	36.5b	(-.f64 (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
	20.4b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
	30.4b	(/.f64 x (-.f64 t (*.f64 a z)))
	10.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
	32.2b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
	10.0b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))

Compiler

Compiled 7086 to 2135 computations (69.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z a))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	0.1b	(/.f64 1 (-.f64 t (*.f64 z a)))
✓	9.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))

series96.0ms (1%)

Counts

4 → 141

Calls

4 calls:

64.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 z a))))
21.0ms	(/.f64 1 (-.f64 t (*.f64 z a)))
5.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 z a))

rewrite121.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

409×	`fma-def_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
249×	`egg-rr`
176×	`fma-neg_binary64`

Counts

4 → 249

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	286	40
2	3693	40
3	5019	40
0	0	0
1	0	0

prune338.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	388	2	390
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	390	11	401

Error

2.6b

Counts

401 → 11

Alt Table

Status	Error	Program
	41.4b	(/.f64 y a)
	34.0b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 2) (-.f64 t (.f64 a z)))
	30.4b	(/.f64 x (-.f64 t (*.f64 a z)))
	30.1b	(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y z) 2)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	32.2b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
▶	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (fma.f64 z (neg.f64 a) t)))
	32.8b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (-.f64 (.f64 t t) (pow.f64 (.f64 z a) 2)) (/.f64 1 (fma.f64 z a t)) (fma.f64 (neg.f64 a) z (.f64 z a))))
	36.5b	(-.f64 (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
	20.4b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
	10.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
	10.0b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))

Compiler

Compiled 9335 to 3389 computations (63.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	0.1b	(/.f64 1 (fma.f64 z (neg.f64 a) t))
✓	9.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (fma.f64 z (neg.f64 a) t)))

series91.0ms (0.9%)

Counts

3 → 105

Calls

3 calls:

63.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (fma.f64 z (neg.f64 a) t)))
20.0ms	(/.f64 1 (fma.f64 z (neg.f64 a) t))
7.0ms	(-.f64 x (*.f64 y z))

rewrite85.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

702×	`prod-diff_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
163×	`egg-rr`
139×	`add-sqr-sqrt_binary64`

Counts

3 → 163

Calls

3 calls:

80.0ms	(-.f64 x (*.f64 y z))
80.0ms	(/.f64 1 (fma.f64 z (neg.f64 a) t))
80.0ms	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (fma.f64 z (neg.f64 a) t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	274	29
2	3172	29
3	5196	29
0	0	0
1	0	0

prune209.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	268	11	279

Error

2.6b

Counts

279 → 11

Alt Table

Status	Error	Program
	41.4b	(/.f64 y a)
	34.0b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 2) (-.f64 t (.f64 a z)))
	30.4b	(/.f64 x (-.f64 t (*.f64 a z)))
	30.1b	(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y z) 2)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	32.2b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
✓	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (fma.f64 z (neg.f64 a) t)))
	32.8b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (-.f64 (.f64 t t) (pow.f64 (.f64 z a) 2)) (/.f64 1 (fma.f64 z a t)) (fma.f64 (neg.f64 a) z (.f64 z a))))
	36.5b	(-.f64 (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
	20.4b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
	10.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
▶	10.0b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))

Compiler

Compiled 7439 to 2662 computations (64.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (.f64 z a))) t)
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 z a)) 2)
✓	9.5b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))
✓	16.7b	(cbrt.f64 (*.f64 z a))

series2.7s (26.5%)

Counts

4 → 144

Calls

4 calls:

944.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (.f64 z a))) t)
911.0ms	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))
420.0ms	(pow.f64 (cbrt.f64 (*.f64 z a)) 2)
389.0ms	(cbrt.f64 (*.f64 z a))

rewrite87.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

318×	`fma-def_binary64`
270×	`expm1-udef_binary64`
270×	`log1p-udef_binary64`
179×	`fma-neg_binary64`
164×	`add-sqr-sqrt_binary64`

Counts

4 → 133

Calls

4 calls:

83.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (.f64 z a))) t)
83.0ms	(pow.f64 (cbrt.f64 (*.f64 z a)) 2)
83.0ms	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))
83.0ms	(cbrt.f64 (*.f64 z a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	324	36
2	3829	32
3	5020	32
0	0	0
1	0	0

prune248.0ms (2.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	342	11	353

Error

2.6b

Counts

353 → 11

Alt Table

Status	Error	Program
	41.4b	(/.f64 y a)
	34.0b	(/.f64 (pow.f64 (sqrt.f64 (-.f64 x (.f64 y z))) 2) (-.f64 t (.f64 a z)))
	30.4b	(/.f64 x (-.f64 t (*.f64 a z)))
	30.1b	(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 y z) 2)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))
	32.2b	(pow.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 z a)))) 2)
✓	9.8b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (fma.f64 z (neg.f64 a) t)))
	31.1b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 z a))) (cbrt.f64 (pow.f64 (*.f64 z a) 2/3)))) t))
	36.5b	(-.f64 (+.f64 (/.f64 (.f64 y t) (.f64 (pow.f64 a 2) z)) (/.f64 y a)) (/.f64 x (*.f64 a z)))
	20.4b	(/.f64 (fma.f64 (cbrt.f64 x) (cbrt.f64 (.f64 x x)) (neg.f64 (.f64 y z))) (-.f64 t (*.f64 a z)))
	10.1b	(pow.f64 (/.f64 (-.f64 t (.f64 z a)) (-.f64 x (.f64 y z))) -1)
✓	10.0b	(/.f64 (-.f64 x (.f64 y z)) (fma.f64 (pow.f64 (cbrt.f64 (.f64 z a)) 2) (neg.f64 (cbrt.f64 (*.f64 z a))) t))

Compiler

Compiled 7803 to 2894 computations (62.9% saved)

regimes2.8s (27.7%)

Accuracy

Total 3.9b remaining (59.1%)

Threshold costs 0b (0%)

Counts

144 → 2

Compiler

Compiled 16562 to 10468 computations (36.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	40	41
2	56	41
3	65	41
4	70	41
5	71	41
6	69	41

end148.0ms (1.5%)

Compiler: Compiled 287 to 175 computations (39% saved)

Details

analyze1.4s (13.6%)

sample1.3s (13.1%)

localize8.0ms (0.1%)

series75.0ms (0.7%)

rewrite125.0ms (1.2%)

prune247.0ms (2.5%)

localize12.0ms (0.1%)

series96.0ms (1%)

rewrite121.0ms (1.2%)

prune338.0ms (3.4%)

localize12.0ms (0.1%)

series91.0ms (0.9%)

rewrite85.0ms (0.8%)

prune209.0ms (2.1%)

localize13.0ms (0.1%)

series2.7s (26.5%)

rewrite87.0ms (0.9%)

prune248.0ms (2.5%)

regimes2.8s (27.7%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end148.0ms (1.5%)

Profiling