Details

analyze964.0ms (5.3%)

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)

sample1.2s (6.5%)

Results

1.1s	8256×	body	128	valid
37.0ms	298×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify93.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

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

9.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.1b	(/.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)

localize11.0ms (0.1%)

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))
✓	11.3b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series168.0ms (0.9%)

Counts

4 → 153

Calls

4 calls:

71.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
46.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
44.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
7.0ms	(-.f64 (*.f64 y z) x)

rewrite92.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

306×	`log1p-udef_binary64`
169×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
157×	`add-log-exp_binary64`

Counts

4 → 152

Calls

4 calls:

88.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
88.0ms	(-.f64 (*.f64 y z) x)
88.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
88.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	67
1	325	67
2	4756	67
3	5258	67

simplify139.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Counts

305 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	7311
1	968	6976
2	4366	6832
3	5125	6832

prune266.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	268	6	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	269	6	275

Error

0.0b

Counts

275 → 6

Alt Table

Status	Error	Program
	9.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
	9.5b	(/.f64 (+.f64 x (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) 2) (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (/.f64 1 (-.f64 (*.f64 z t) x))))) (+.f64 x 1))
▶	1.1b	(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)))
	26.6b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	18.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	34.3b	(.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) (.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) (/.f64 1 (+.f64 x 1))))

Compiler

Compiled 9492 to 3806 computations (59.9% saved)

localize14.0ms (0.1%)

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)))
✓	3.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	7.6b	(/.f64 z (-.f64 (*.f64 t z) x))

series118.0ms (0.7%)

Counts

4 → 144

Calls

4 calls:

72.0ms	(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)))
21.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
16.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
8.0ms	(/.f64 y (+.f64 x 1))

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

322×	`log1p-udef_binary64`
178×	`add-sqr-sqrt_binary64`
168×	`log1p-expm1-u_binary64`
168×	`expm1-log1p-u_binary64`
165×	`add-log-exp_binary64`

Counts

4 → 126

Calls

4 calls:

80.0ms	(/.f64 y (+.f64 x 1))
80.0ms	(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)))
80.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
80.0ms	(/.f64 z (-.f64 (*.f64 t z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	344	65
2	4891	65
3	5421	65

simplify105.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

270 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	5576
1	815	5380
2	3635	5259
3	5134	5259

prune243.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	220	7	227

Error

Counts

227 → 7

Alt Table

Status	Error	Program
	9.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
	9.5b	(/.f64 (+.f64 x (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) 2) (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (/.f64 1 (-.f64 (*.f64 z t) x))))) (+.f64 x 1))
✓	1.1b	(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)))
▶	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (/.f64 (-.f64 (.f64 z t) x) z) -1) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	26.6b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	18.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	34.3b	(.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) (.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) (/.f64 1 (+.f64 x 1))))

Compiler

Compiled 8664 to 3592 computations (58.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (/.f64 (-.f64 (.f64 z t) x) z) -1) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	0.3b	(pow.f64 (/.f64 (-.f64 (*.f64 z t) x) z) -1)
	3.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	7.5b	(/.f64 (-.f64 (*.f64 z t) x) z)

series106.0ms (0.6%)

Counts

3 → 120

Calls

3 calls:

77.0ms

(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (/.f64 (-.f64 (*.f64 z t) x) z) -1) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

19.0ms

(pow.f64 (/.f64 (-.f64 (*.f64 z t) x) z) -1)

10.0ms

(/.f64 (-.f64 (*.f64 z t) x) z)

rewrite127.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

729×	`prod-diff_binary64`
296×	`egg-rr`
202×	`add-sqr-sqrt_binary64`
191×	`log1p-expm1-u_binary64`
191×	`expm1-log1p-u_binary64`

Counts

3 → 296

Calls

3 calls:

117.0ms

(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (/.f64 (-.f64 (*.f64 z t) x) z) -1) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

117.0ms

(pow.f64 (/.f64 (-.f64 (*.f64 z t) x) z) -1)

117.0ms

(/.f64 (-.f64 (*.f64 z t) x) z)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	398	58
2	4806	58
3	6337	58

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

628×	`cancel-sign-sub-inv_binary64`
308×	`times-frac_binary64`
275×	`sub-neg_binary64`
227×	`associate-/l*_binary64`
223×	`associate-+r+_binary64`

Counts

416 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	4480
1	721	4314
2	3319	4235
3	5065	4235

prune406.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	414	7	421

Error

Counts

421 → 7

Alt Table

Status	Error	Program
▶	9.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
	9.5b	(/.f64 (+.f64 x (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) 2) (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (/.f64 1 (-.f64 (*.f64 z t) x))))) (+.f64 x 1))
✓	1.1b	(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)))
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (/.f64 (-.f64 (.f64 z t) x) z) -1) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	26.6b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	18.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	34.3b	(.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) (.f64 (sqrt.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) (/.f64 1 (+.f64 x 1))))

Compiler

Compiled 22071 to 7211 computations (67.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.1b	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))))
✓	0.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
✓	11.3b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))

series10.8s (59.4%)

Counts

3 → 144

Calls

3 calls:

10.4s

(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x)))) -1)

406.0ms

(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x))))

40.0ms

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

rewrite87.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

333×	`log1p-udef_binary64`
188×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
174×	`add-cbrt-cube_binary64`

Counts

3 → 110

Calls

3 calls:

84.0ms

(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x))))

84.0ms

(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 z t) x)))) -1)

84.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	69
1	367	66
2	4780	66
3	5285	66

simplify610.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

254 → 197

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5092	106653

prune1.5s (8.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	241	7	248

Error

Counts

248 → 7

Alt Table

Status	Error	Program
✓	9.1b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
	9.5b	(/.f64 (+.f64 x (.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) 2) (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (/.f64 1 (-.f64 (*.f64 z t) x))))) (+.f64 x 1))
✓	1.1b	(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)))
✓	1.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (/.f64 (-.f64 (.f64 z t) x) z) -1) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	26.6b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	22.2b	(.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (fma.f64 x x -1)) (+.f64 x -1))
	18.7b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))

Compiler

Compiled 71288 to 45354 computations (36.4% saved)

regimes835.0ms (4.6%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

159 → 1

Compiler

Compiled 19145 to 12122 computations (36.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	28	38
2	39	38
3	45	38
4	48	38
5	47	38

end114.0ms (0.6%)

Compiler: Compiled 234 to 145 computations (38% saved)

Details

analyze964.0ms (5.3%)

sample1.2s (6.5%)

simplify93.0ms (0.5%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series168.0ms (0.9%)

rewrite92.0ms (0.5%)

simplify139.0ms (0.8%)

prune266.0ms (1.5%)

localize14.0ms (0.1%)

series118.0ms (0.7%)

rewrite83.0ms (0.5%)

simplify105.0ms (0.6%)

prune243.0ms (1.3%)

localize17.0ms (0.1%)

series106.0ms (0.6%)

rewrite127.0ms (0.7%)

simplify101.0ms (0.6%)

prune406.0ms (2.2%)

localize11.0ms (0.1%)

series10.8s (59.4%)

rewrite87.0ms (0.5%)

simplify610.0ms (3.4%)

prune1.5s (8.1%)

regimes835.0ms (4.6%)

simplify3.0ms (0%)

end114.0ms (0.6%)

Profiling