Details

analyze984.0ms (12.2%)

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)

sample90.0ms (1.1%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify93.0ms (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

6.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.2b	(/.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 t z) x)
✓	0.7b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	7.8b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series204.0ms (2.5%)

Counts

4 → 153

Calls

4 calls:

94.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
54.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
48.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
7.0ms	(-.f64 (*.f64 t z) x)

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

12.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
10.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 t z) x)

simplify152.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
218×	`fma-def_binary64`

Counts

268 → 293

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	10265
1	1359	9717
2	5098	9717

prune306.0ms (3.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	288	5	293
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	289	5	294

Error

Counts

294 → 5

Alt Table

Status	Error	Program
	6.2b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
	6.2b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	12.8b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)) 3))) (+.f64 x 1))
▶	0.7b	(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)))
	22.9b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))

Compiler

Compiled 10642 to 3940 computations (63% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.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)))
✓	1.5b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	5.8b	(/.f64 z (-.f64 (*.f64 t z) x))

series134.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

88.0ms	(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)))
24.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
22.0ms	(/.f64 x (-.f64 (*.f64 t z) x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
0.0ms	(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)))

simplify189.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

400×	`times-frac_binary64`
326×	`fma-neg_binary64`
313×	`associate-/l*_binary64`
305×	`sub-neg_binary64`
241×	`associate-+r+_binary64`

Counts

192 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6888
1	973	6477
2	4210	6352
3	4995	6350
4	5047	6350

prune276.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	264	5	269

Error

Counts

269 → 5

Alt Table

Status	Error	Program
	6.2b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
▶	6.2b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	12.8b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)) 3))) (+.f64 x 1))
	16.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	0.7b	(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)))

Compiler

Compiled 10269 to 3909 computations (61.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.4b	(/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))
✓	0.7b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	8.0b	(/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x))

series228.0ms (2.8%)

Counts

3 → 144

Calls

3 calls:

93.0ms

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

74.0ms

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

61.0ms

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

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`times-frac_binary64`
93×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

3 → 167

Calls

3 calls:

21.0ms

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

12.0ms

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

7.0ms

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

simplify188.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary64`
389×	`associate-/l*_binary64`
324×	`associate-/r*_binary64`
266×	`associate--l+_binary64`
179×	`sub-neg_binary64`

Counts

311 → 360

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	480	13006
1	1499	12060
2	5108	12060

prune390.0ms (4.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	387	0	387
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	387	5	392

Error

Counts

392 → 5

Alt Table

Status	Error	Program
▶	6.2b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
✓	6.2b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	12.8b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)) 3))) (+.f64 x 1))
	16.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	0.7b	(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)))

Compiler

Compiled 14387 to 5528 computations (61.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
✓	0.8b	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))
	7.8b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series844.0ms (10.5%)

Counts

2 → 96

Calls

2 calls:

738.0ms	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))
105.0ms	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`*-un-lft-identity_binary64`
146×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
42×	`distribute-lft-out_binary64`

Counts

2 → 156

Calls

2 calls:

16.0ms	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
14.0ms	(/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))))

simplify450.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
514×	`+-commutative_binary64`
450×	`associate-+r+_binary64`
275×	`*-commutative_binary64`
221×	`associate-/r*_binary64`

Counts

252 → 264

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1257	25754
1	4648	25408
2	5344	25408

prune686.0ms (8.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	386	0	386
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	386	5	391

Error

Counts

391 → 5

Alt Table

Status	Error	Program
✓	6.2b	(/.f64 1 (/.f64 (+.f64 x 1) (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))))
✓	6.2b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	12.8b	(/.f64 (+.f64 x (cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)) 3))) (+.f64 x 1))
	16.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	0.7b	(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)))

Compiler

Compiled 32027 to 15258 computations (52.4% saved)

regimes1.6s (19.8%)

Accuracy

Total 1.9b remaining (98.9%)

Threshold costs 0b (0%)

Counts

209 → 1

Compiler

Compiled 23399 to 15196 computations (35.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	23	38
2	31	38
3	35	38
4	37	38
5	36	38

end1.0ms (0%)

Compiler: Compiled 30 to 16 computations (46.7% saved)

sample1.0s (12.6%)

Algorithm

1×

intervals

Results

535.0ms	8000×	body	128	valid
38.0ms	339×	body	128	invalid

Compiler

Compiled 173 to 108 computations (37.6% saved)

Details

analyze984.0ms (12.2%)

sample90.0ms (1.1%)

simplify93.0ms (1.2%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series204.0ms (2.5%)

rewrite39.0ms (0.5%)

simplify152.0ms (1.9%)

prune306.0ms (3.8%)

localize13.0ms (0.2%)

series134.0ms (1.7%)

rewrite12.0ms (0.2%)

simplify189.0ms (2.3%)

prune276.0ms (3.4%)

localize14.0ms (0.2%)

series228.0ms (2.8%)

rewrite56.0ms (0.7%)

simplify188.0ms (2.3%)

prune390.0ms (4.8%)

localize17.0ms (0.2%)

series844.0ms (10.5%)

rewrite54.0ms (0.7%)

simplify450.0ms (5.6%)

prune686.0ms (8.5%)

regimes1.6s (19.8%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.0s (12.6%)

Profiling