Details

analyze994.0ms (13.3%)

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 (16.3%)

Results

1.1s	8256×	body	128	valid
45.0ms	357×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify92.0ms (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

7.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.5b	(/.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.1b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series153.0ms (2%)

Counts

3 → 105

Calls

3 calls:

93.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
54.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
6.0ms	(-.f64 (*.f64 t z) x)

rewrite89.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

110× egg-rr

Counts

3 → 110

Calls

2 calls:

86.0ms	((/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) (-.f64 (*.f64 t z) x))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	325	48
2	4756	48
3	5258	48
0	0	0
1	0	0

simplify109.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

933×	`cancel-sign-sub-inv_binary64`
447×	`sub-neg_binary64`
341×	`times-frac_binary64`
262×	`+-commutative_binary64`
255×	`associate-+r+_binary64`

Counts

215 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	5463
1	866	5176
2	3935	5071
3	5860	5071

prune221.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	189	8	197
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	8	198

Error

0.0b

Counts

198 → 8

Alt Table

Status	Error	Program
	7.6b	(pow.f64 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x)))) -1)
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 (.f64 z t) x)) 2)) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 z t) x))))) (+.f64 x 1))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	20.5b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
	8.0b	(/.f64 (+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (-.f64 (.f64 z t) x)))) (+.f64 x 1))
▶	2.3b	(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)))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (sqrt.f64 (+.f64 x 1))))
	25.2b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 7173 to 3109 computations (56.7% 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)))
✓	2.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	6.8b	(/.f64 z (-.f64 (*.f64 t z) x))

series135.0ms (1.8%)

Counts

4 → 144

Calls

4 calls:

83.0ms	(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))
21.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
9.0ms	(/.f64 y (+.f64 x 1))

rewrite99.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

122× egg-rr

Counts

4 → 122

Calls

2 calls:

96.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify106.0ms (1.4%)

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

266 → 218

Iterations

Useful iterations: 2 (0.0ms)

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

prune271.0ms (3.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	215	3	218
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	218	8	226

Error

Counts

226 → 8

Alt Table

Status	Error	Program
	2.3b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (pow.f64 (/.f64 (-.f64 (.f64 z t) x) x) -1)) (+.f64 x 1)))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	20.5b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
▶	2.3b	(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)))
	8.0b	(/.f64 (+.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) 2) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (-.f64 (.f64 z t) x)))) (+.f64 x 1))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 (.f64 z t) x)) 2)) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 z t) x))))) (+.f64 x 1))
	39.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (/.f64 z (-.f64 (pow.f64 (.f64 z t) 3) (pow.f64 x 3))) (+.f64 (pow.f64 (.f64 z t) 2) (.f64 x (+.f64 x (.f64 z t))))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 8730 to 3673 computations (57.9% saved)

localize16.0ms (0.2%)

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)))
✓	0.7b	(pow.f64 (/.f64 (-.f64 (*.f64 z t) x) z) -1)
	2.4b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	6.8b	(/.f64 (-.f64 (*.f64 z t) x) z)

series118.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

87.0ms

(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)))

22.0ms

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

9.0ms

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

rewrite126.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

294× egg-rr

Counts

3 → 294

Calls

2 calls:

116.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

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

simplify155.0ms (2.1%)

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

414 → 363

Iterations

Useful iterations: 2 (0.0ms)

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

prune1.2s (16.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	410	1	411
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	411	8	419

Error

Counts

419 → 8

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (pow.f64 (/.f64 (-.f64 (.f64 z t) x) x) -1)) (+.f64 x 1)))
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	20.5b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
✓	2.3b	(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)))
	2.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (pow.f64 (cbrt.f64 (/.f64 z (-.f64 (.f64 z t) x))) 2) (cbrt.f64 (/.f64 z (-.f64 (.f64 z t) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 (.f64 z t) x)) 2)) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 z t) x))))) (+.f64 x 1))
	39.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (/.f64 z (-.f64 (pow.f64 (.f64 z t) 3) (pow.f64 x 3))) (+.f64 (pow.f64 (.f64 z t) 2) (.f64 x (+.f64 x (.f64 z t))))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 22151 to 7294 computations (67.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (pow.f64 (/.f64 (-.f64 (.f64 z t) x) x) -1)) (+.f64 x 1)))
✓	0.5b	(pow.f64 (/.f64 (-.f64 (*.f64 z t) x) x) -1)
✓	2.1b	(/.f64 (-.f64 (*.f64 z t) x) x)
	6.8b	(/.f64 z (-.f64 (*.f64 t z) x))

series124.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

90.0ms

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

23.0ms

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

11.0ms

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

rewrite229.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

78× egg-rr

Counts

3 → 78

Calls

2 calls:

227.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	64
1	398	58
2	4782	58
3	5796	58
0	0	0
1	0	0

simplify92.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

621×	`cancel-sign-sub-inv_binary64`
312×	`times-frac_binary64`
273×	`sub-neg_binary64`
228×	`associate-/l*_binary64`
222×	`associate-+r+_binary64`

Counts

198 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	4593
1	711	4403
2	3314	4267
3	5041	4267

prune399.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	195	7	202

Error

Counts

202 → 7

Alt Table

Status	Error	Program
	19.9b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	20.5b	(/.f64 (+.f64 x (pow.f64 (sqrt.f64 (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 z t) x))) 2)) (+.f64 x 1))
✓	2.3b	(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)))
	7.9b	(/.f64 (+.f64 x (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (-.f64 (.f64 z t) x)) 2)) (/.f64 (-.f64 (.f64 y z) x) (cbrt.f64 (-.f64 (.f64 z t) x))))) (+.f64 x 1))
	39.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (/.f64 z (-.f64 (pow.f64 (.f64 z t) 3) (pow.f64 x 3))) (+.f64 (pow.f64 (.f64 z t) 2) (.f64 x (+.f64 x (.f64 z t))))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	20.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 z t) x))) (sqrt.f64 (+.f64 x 1))))
	2.6b	(fma.f64 (/.f64 y (+.f64 x 1)) (pow.f64 (cbrt.f64 (/.f64 z (-.f64 (.f64 z t) x))) 3) (/.f64 (-.f64 x (pow.f64 (/.f64 (-.f64 (.f64 z t) x) x) -1)) (+.f64 x 1)))

Compiler

Compiled 7797 to 3469 computations (55.5% saved)

regimes1.3s (17.4%)

Accuracy

Total 0.1b remaining (81.4%)

Threshold costs 0.1b (81.4%)

Counts

150 → 1

Compiler

Compiled 22185 to 13642 computations (38.5% 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

end139.0ms (1.9%)

Compiler: Compiled 274 to 171 computations (37.6% saved)

Details

analyze994.0ms (13.3%)

sample1.2s (16.3%)

simplify92.0ms (1.2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series153.0ms (2%)

rewrite89.0ms (1.2%)

simplify109.0ms (1.5%)

prune221.0ms (3%)

localize13.0ms (0.2%)

series135.0ms (1.8%)

rewrite99.0ms (1.3%)

simplify106.0ms (1.4%)

prune271.0ms (3.6%)

localize16.0ms (0.2%)

series118.0ms (1.6%)

rewrite126.0ms (1.7%)

simplify155.0ms (2.1%)

prune1.2s (16.6%)

localize16.0ms (0.2%)

series124.0ms (1.7%)

rewrite229.0ms (3.1%)

simplify92.0ms (1.2%)

prune399.0ms (5.3%)

regimes1.3s (17.4%)

simplify3.0ms (0%)

end139.0ms (1.9%)

Profiling