Details

analyze946.0ms (12.3%)

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 (15.4%)

Results

1.1s	8256×	body	128	valid
41.0ms	354×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify95.0ms (1.2%)

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

9.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.3b	(/.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 (0.1%)

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 t z) x)
✓	1.2b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	10.1b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series149.0ms (1.9%)

Counts

4 → 153

Calls

4 calls:

67.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
38.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
38.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 t z) x)

rewrite97.0ms (1.3%)

Algorithm

2×	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:

93.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
93.0ms	(-.f64 (*.f64 t z) x)
93.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
93.0ms	(/.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
0	0	0
1	0	0

simplify148.0ms (1.9%)

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 → 273

Iterations

Useful iterations: 2 (0.0ms)

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

prune265.0ms (3.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	268	5	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	269	5	274

Error

0.0b

Counts

274 → 5

Alt Table

Status	Error	Program
▶	3.5b	(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)))
	19.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
	26.4b	(-.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 y (.f64 t (+.f64 x 1)))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1)))))
	25.8b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	19.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)

Compiler

Compiled 9427 to 3787 computations (59.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
✓	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)))
✓	2.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.5b	(/.f64 z (-.f64 (*.f64 t z) x))

series118.0ms (1.5%)

Counts

4 → 156

Calls

4 calls:

74.0ms	(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)))
16.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
14.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
13.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))

rewrite95.0ms (1.2%)

Algorithm

2×	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 → 130

Calls

4 calls:

91.0ms	(-.f64 x (/.f64 x (-.f64 (*.f64 t z) x)))
91.0ms	(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)))
91.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
91.0ms	(/.f64 z (-.f64 (*.f64 t z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	71
1	344	71
2	4891	71
3	5421	71
0	0	0
1	0	0

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
319×	`times-frac_binary64`
313×	`sub-neg_binary64`
259×	`associate-+r+_binary64`
239×	`+-commutative_binary64`

Counts

286 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	6089
1	810	5899
2	3644	5754
3	5136	5754

prune211.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	228	6	234

Error

0.0b

Counts

234 → 6

Alt Table

Status	Error	Program
	26.2b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (sqrt.f64 (/.f64 z (-.f64 (.f64 z t) x))) 2) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	3.5b	(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)))
	19.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
	20.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	25.8b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
▶	19.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)

Compiler

Compiled 9199 to 3770 computations (59% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1)))
✓	0.1b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)
✓	1.2b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))
✓	10.1b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))

series608.0ms (7.9%)

Counts

4 → 176

Calls

4 calls:

321.0ms	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)
191.0ms	(sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1)))
60.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))
35.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))

rewrite89.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

332×	`log1p-udef_binary64`
185×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
175×	`add-log-exp_binary64`

Counts

4 → 142

Calls

4 calls:

85.0ms	(sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1)))
85.0ms	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)
85.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))
85.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	93
1	372	93
2	4836	93
3	5324	93
0	0	0
1	0	0

simplify682.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

384×	`*-commutative_binary64`
373×	`+-commutative_binary64`
303×	`associate-+r+_binary64`
226×	`fma-def_binary64`
208×	`sub-neg_binary64`

Counts

318 → 266

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1099	21216
1	4085	20814
2	4967	20814
3	4974	20814

prune567.0ms (7.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	266	6	272

Error

0.0b

Counts

272 → 6

Alt Table

Status	Error	Program
	26.2b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (sqrt.f64 (/.f64 z (-.f64 (.f64 z t) x))) 2) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	3.5b	(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)))
▶	19.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
	20.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	25.8b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
✓	19.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)

Compiler

Compiled 23269 to 13259 computations (43% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
✓	3.2b	(-.f64 (pow.f64 (.f64 z t) 2) (.f64 x x))
✓	10.1b	(/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))
✓	32.1b	(/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 x x)))

series330.0ms (4.3%)

Counts

4 → 168

Calls

4 calls:

193.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
97.0ms	(/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))
21.0ms	(/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 x x)))
18.0ms	(-.f64 (pow.f64 (.f64 z t) 2) (.f64 x x))

rewrite98.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`prod-diff_binary64`
233×	`add-sqr-sqrt_binary64`
228×	`log1p-expm1-u_binary64`
228×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`

Counts

4 → 106

Calls

4 calls:

94.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
94.0ms	(-.f64 (pow.f64 (.f64 z t) 2) (.f64 x x))
94.0ms	(/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))
94.0ms	(/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (.f64 x x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	106
1	469	98
2	4746	98
3	5089	98
0	0	0
1	0	0

simplify163.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

489×	`sub-neg_binary64`
379×	`times-frac_binary64`
296×	`fma-neg_binary64`
293×	`associate-/l*_binary64`
290×	`+-commutative_binary64`

Counts

274 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	8751
1	1002	8431
2	4419	8326
3	5222	8326

prune213.0ms (2.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	210	6	216

Error

0.0b

Counts

216 → 6

Alt Table

Status	Error	Program
	26.2b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (sqrt.f64 (/.f64 z (-.f64 (.f64 z t) x))) 2) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	3.5b	(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)))
✓	19.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (/.f64 1 (/.f64 (fma.f64 z t x) (-.f64 (pow.f64 (.f64 z t) 2) (*.f64 x x)))))) (+.f64 x 1))
	20.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	25.8b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
✓	19.3b	(pow.f64 (sqrt.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) (+.f64 x 1))) 2)

Compiler

Compiled 9413 to 4364 computations (53.6% saved)

regimes1.3s (17.2%)

Accuracy

Total 0.1b remaining (84.6%)

Threshold costs 0.1b (84.6%)

Counts

181 → 4

Compiler

Compiled 21295 to 13862 computations (34.9% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
7×	`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	38	201
1	50	201
2	63	201
3	69	201
4	72	201
5	71	201

end120.0ms (1.6%)

Compiler: Compiled 433 to 207 computations (52.2% saved)

Details

analyze946.0ms (12.3%)

sample1.2s (15.4%)

simplify95.0ms (1.2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series149.0ms (1.9%)

rewrite97.0ms (1.3%)

simplify148.0ms (1.9%)

prune265.0ms (3.5%)

localize13.0ms (0.2%)

series118.0ms (1.5%)

rewrite95.0ms (1.2%)

simplify118.0ms (1.5%)

prune211.0ms (2.7%)

localize13.0ms (0.2%)

series608.0ms (7.9%)

rewrite89.0ms (1.2%)

simplify682.0ms (8.9%)

prune567.0ms (7.4%)

localize18.0ms (0.2%)

series330.0ms (4.3%)

rewrite98.0ms (1.3%)

simplify163.0ms (2.1%)

prune213.0ms (2.8%)

regimes1.3s (17.2%)

bsearch8.0ms (0.1%)

simplify7.0ms (0.1%)

end120.0ms (1.6%)

Profiling