Details

analyze951.0ms (15.6%)

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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.1s (18.2%)

Results

1.0s	8256×	body	128	valid
44.0ms	340×	body	128	invalid

Compiler

Compiled 44 to 28 computations (36.4% saved)

preprocess34.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

513×	`distribute-rgt-in_binary64`
482×	`fma-def_binary64`
472×	`div-sub_binary64`
360×	`fma-neg_binary64`
312×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	175
1	123	175
2	214	175
3	436	175
4	1062	175
5	2449	175
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

507×	`times-frac_binary64`
351×	`fma-def_binary64`
333×	`associate-/l*_binary64`
262×	`div-sub_binary64`
250×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	202	25
5	448	25
6	1376	25

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

8.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	11.5b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series166.0ms (2.7%)

Counts

4 → 153

Calls

45 calls:

12.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	y	-inf
10.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	x	0
9.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))	z	-inf
8.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))	y	-inf
7.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))	y	inf

rewrite47.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

169×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
160×	`add-cbrt-cube_binary64`
156×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	325	67

Stop Event

1×	node limit

Counts

4 → 148

simplify119.0ms (2%)

Algorithm

1×	egg-herbie

Rules

585×	`sub-neg_binary64`
341×	`times-frac_binary64`
308×	`+-commutative_binary64`
295×	`associate-+r+_binary64`
289×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	7311
1	991	6976
2	4508	6832

Stop Event

1×	node limit

Counts

301 → 270

prune281.0ms (4.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	264	6	270
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	6	271

Error

Counts

271 → 6

Alt Table

Status	Error	Program
▶	2.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	4.1b	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	8.3b	(/.f64 (fma.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (.f64 z t) x)) x) (+.f64 x 1))
	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))) (/.f64 x (+.f64 1 x))) (/.f64 x (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))))
	20.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	17.8b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))

Compiler

Compiled 9416 to 3832 computations (59.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x 1))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	4.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.9b	(/.f64 z (-.f64 (*.f64 t z) x))

series108.0ms (1.8%)

Counts

4 → 144

Calls

36 calls:

8.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	t	0
8.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	y	inf
7.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	y	-inf
7.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	x	-inf
6.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))	y	0

rewrite40.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

178×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`
164×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	344	65

Stop Event

1×	node limit

Counts

4 → 122

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

685×	`cancel-sign-sub-inv_binary64`
319×	`times-frac_binary64`
311×	`sub-neg_binary64`
241×	`associate-+r+_binary64`
239×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	5576
1	824	5380
2	3743	5259

Stop Event

1×	node limit

Counts

266 → 218

prune245.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	218	6	224

Error

Counts

224 → 6

Alt Table

Status	Error	Program
✓	2.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	4.1b	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	8.3b	(/.f64 (fma.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (.f64 z t) x)) x) (+.f64 x 1))
	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))) (/.f64 x (+.f64 1 x))) (/.f64 x (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))))
	20.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	17.8b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))

Compiler

Compiled 8514 to 3560 computations (58.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
✓	2.7b	(/.f64 (-.f64 (*.f64 t z) x) y)
	4.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	10.4b	(/.f64 z (/.f64 (-.f64 (*.f64 t z) x) y))

series118.0ms (1.9%)

Counts

3 → 136

Calls

36 calls:

10.0ms	(/.f64 z (/.f64 (-.f64 (*.f64 t z) x) y))	x	inf
8.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	t	0
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	y	-inf
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	y	inf
6.0ms	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))	x	0

rewrite36.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

192×	`add-sqr-sqrt_binary64`
184×	`log1p-expm1-u_binary64`
184×	`expm1-log1p-u_binary64`
183×	`add-cbrt-cube_binary64`
178×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	365	57

Stop Event

1×	node limit

Counts

3 → 83

simplify93.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

712×	`cancel-sign-sub-inv_binary64`
326×	`times-frac_binary64`
302×	`sub-neg_binary64`
239×	`associate-/l*_binary64`
237×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	5116
1	786	4829
2	3627	4669

Stop Event

1×	node limit

Counts

219 → 157

prune228.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	205	6	211

Error

Counts

211 → 6

Alt Table

Status	Error	Program
✓	2.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	4.1b	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	8.3b	(/.f64 (fma.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (.f64 z t) x)) x) (+.f64 x 1))
	15.1b	(/.f64 (+.f64 x (-.f64 (/.f64 y t) (/.f64 x (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
▶	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))) (/.f64 x (+.f64 1 x))) (/.f64 x (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))))
	20.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))

Compiler

Compiled 7640 to 2981 computations (61% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))) (/.f64 x (+.f64 1 x)))
✓	0.0b	(.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))
✓	12.9b	(/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x)))
✓	15.9b	(/.f64 x (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x)))

series262.0ms (4.3%)

Counts

4 → 161

Calls

42 calls:

25.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x)))	y	-inf
22.0ms	(/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x)))	y	inf
14.0ms	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))) (/.f64 x (+.f64 1 x)))	y	inf
12.0ms	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))) (/.f64 x (+.f64 1 x)))	y	-inf
12.0ms	(+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))) (/.f64 x (+.f64 1 x)))	t	0

rewrite59.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

183×	`egg-rr`
178×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
168×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	76
1	348	74

Stop Event

1×	node limit

Counts

4 → 183

simplify122.0ms (2%)

Algorithm

1×	egg-herbie

Rules

754×	`times-frac_binary64`
519×	`associate-/r*_binary64`
457×	`associate-/l*_binary64`
246×	`fma-def_binary64`
191×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	414	10811
1	1529	9678

Stop Event

1×	node limit

Counts

344 → 308

prune428.0ms (7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	343	1	344
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	345	5	350

Error

Counts

350 → 5

Alt Table

Status	Error	Program
	15.0b	(-.f64 (+.f64 (/.f64 y (fma.f64 x t t)) (/.f64 x (+.f64 1 x))) (/.f64 x (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))))
✓	4.1b	(/.f64 (+.f64 x (-.f64 (/.f64 z (/.f64 (-.f64 (.f64 t z) x) y)) (/.f64 x (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	8.3b	(/.f64 (fma.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (.f64 z t) x)) x) (+.f64 x 1))
✓	8.3b	(-.f64 (+.f64 (/.f64 (.f64 y z) (.f64 (+.f64 1 x) (-.f64 (.f64 t z) x))) (/.f64 x (+.f64 1 x))) (/.f64 x (.f64 (+.f64 1 x) (-.f64 (*.f64 t z) x))))
	20.1b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))

Compiler

Compiled 18455 to 9229 computations (50% saved)

regimes1.3s (22%)

Accuracy

Total 1.9b remaining (89.9%)

Threshold costs 0b (0%)

Counts

188 → 2

Compiler

Compiled 23165 to 14587 computations (37% saved)

bsearch29.0ms (0.5%)

Algorithm

1×	binary-search

Calls

1 calls:

22.0ms

Steps

Iters	Point		Range
4.21312888900773e-16	∈ [	9.06099515116754e-24	,	4.268538385257724e-16	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	75
1	39	75
2	51	75
3	57	75
4	60	75

Stop Event

1×

saturated

end92.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 246 to 139 computations (43.5% saved)

Details

analyze951.0ms (15.6%)

sample1.1s (18.2%)

preprocess34.0ms (0.6%)

simplify22.0ms (0.4%)

prune2.0ms (0%)

localize10.0ms (0.2%)

series166.0ms (2.7%)

rewrite47.0ms (0.8%)

simplify119.0ms (2%)

prune281.0ms (4.6%)

localize13.0ms (0.2%)

series108.0ms (1.8%)

rewrite40.0ms (0.7%)

simplify97.0ms (1.6%)

prune245.0ms (4%)

localize11.0ms (0.2%)

series118.0ms (1.9%)

rewrite36.0ms (0.6%)

simplify93.0ms (1.5%)

prune228.0ms (3.8%)

localize13.0ms (0.2%)

series262.0ms (4.3%)

rewrite59.0ms (1%)

simplify122.0ms (2%)

prune428.0ms (7%)

regimes1.3s (22%)

bsearch29.0ms (0.5%)

simplify4.0ms (0.1%)

end92.0ms (1.5%)

Profiling