Details

analyze1.3s (18.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.6s (36.9%)

Results

969.0ms	6339×	body	128	valid
660.0ms	1005×	body	1024	valid
271.0ms	605×	body	512	valid
203.0ms	1530×	body	128	invalid
126.0ms	208×	body	1024	invalid
112.0ms	254×	body	512	invalid
92.0ms	302×	body	256	valid
42.0ms	147×	body	256	invalid
6.0ms	5×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
522×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
256×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	56	16
4	119	16
5	280	16
6	672	16
7	2284	16
8	4398	16
9	4953	16

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

4.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.4b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	4.4b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series182.0ms (2.6%)

Counts

4 → 108

Calls

4 calls:

96.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
47.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
30.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
8.0ms	(/.f64 y (+.f64 y z))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
82×	`add-sqr-sqrt_binary64`
82×	`add-cube-cbrt_binary64`

Counts

4 → 195

Calls

4 calls:

16.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
9.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
5.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
3.0ms	(/.f64 y (+.f64 y z))

simplify205.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

385×	`fma-def_binary64`
358×	`times-frac_binary64`
355×	`associate-/l*_binary64`
264×	`associate-/r*_binary64`
248×	`associate-r_binary64`

Counts

303 → 430

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	612	9531
1	1653	9295
2	5034	9295

prune317.0ms (4.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	427	3	430
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	428	3	431

Error

0.0b

Counts

431 → 3

Alt Table

Status	Error	Program
	9.9b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	1.9b	(+.f64 x (/.f64 1 y))
	31.0b	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))

Compiler

Compiled 12581 to 4723 computations (62.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
448×	`fma-neg_binary64`
321×	`fma-def_binary64`
284×	`distribute-rgt-in_binary64`
282×	`associate-+l+_binary64`

Counts

42 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	322
1	88	302
2	189	299
3	419	299
4	1068	299
5	2246	299
6	3475	299
7	4871	299
8	4894	299
9	4906	299

prune15.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Error

0.0b

Counts

31 → 3

Alt Table

Status	Error	Program
▶	9.9b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.9b	(+.f64 x (/.f64 1 y))
	31.0b	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))

Compiler

Compiled 384 to 248 computations (35.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	0.0b	(/.f64 (exp.f64 (neg.f64 z)) y)

series20.0ms (0.3%)

Counts

2 → 44

Calls

2 calls:

12.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
8.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

5.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
4.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-/l*_binary64`
517×	`fma-neg_binary64`
466×	`fma-def_binary64`
340×	`associate-/l/_binary64`
311×	`associate-*l/_binary64`

Counts

92 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	1172
1	240	1134
2	585	1126
3	1543	1124
4	4396	1117
5	4890	1117
6	4978	1117

prune40.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	81	3	84

Error

0.0b

Counts

84 → 3

Alt Table

Status	Error	Program
✓	9.9b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.9b	(+.f64 x (/.f64 1 y))
▶	31.0b	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))

Compiler

Compiled 1197 to 408 computations (65.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.4b	(-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y)))
✓	4.4b	(pow.f64 (/.f64 y (+.f64 z y)) (*.f64 2 y))
✓	4.4b	(pow.f64 (/.f64 y (+.f64 z y)) y)
✓	28.6b	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))

series501.0ms (7.2%)

Counts

4 → 120

Calls

4 calls:

283.0ms	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))
153.0ms	(-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y)))
32.0ms	(pow.f64 (/.f64 y (+.f64 z y)) y)
32.0ms	(pow.f64 (/.f64 y (+.f64 z y)) (*.f64 2 y))

rewrite104.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

264×	`times-frac_binary64`
241×	`add-sqr-sqrt_binary64`
112×	`unpow-prod-down_binary64`
102×	`*-un-lft-identity_binary64`
100×	`difference-of-squares_binary64`

Counts

4 → 247

Calls

4 calls:

34.0ms	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))
14.0ms	(-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y)))
5.0ms	(pow.f64 (/.f64 y (+.f64 z y)) (*.f64 2 y))
5.0ms	(pow.f64 (/.f64 y (+.f64 z y)) y)

simplify498.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

349×	`*-commutative_binary64`
308×	`+-commutative_binary64`
221×	`associate-+r+_binary64`
170×	`fma-def_binary64`
157×	`associate-*r/_binary64`

Counts

367 → 584

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1458	28404
1	4704	27635
2	4965	27635
3	4974	27635

prune533.0ms (7.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	583	1	584
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	583	4	587

Error

Counts

587 → 4

Alt Table

Status	Error	Program
	49.2b	(*.f64 (/.f64 (+.f64 x (/.f64 (fabs.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y)) (+.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))) (/.f64 (-.f64 x (/.f64 (fabs.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y)) (-.f64 (sqrt.f64 x) (sqrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))))
✓	9.9b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.9b	(+.f64 x (/.f64 1 y))
✓	31.0b	(/.f64 (-.f64 (.f64 x x) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) (.f64 2 y)) (*.f64 y y))) (-.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)))

Compiler

Compiled 40823 to 16375 computations (59.9% saved)

regimes279.0ms (4%)

Accuracy

Total 1.6b remaining (98.8%)

Threshold costs 0b (0%)

Counts

36 → 3

Compiler

Compiled 4192 to 2292 computations (45.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	75
1	35	75
2	37	75
3	38	75
4	37	75

end74.0ms (1.1%)

Compiler: Compiled 210 to 99 computations (52.9% saved)

Details

analyze1.3s (18.5%)

sample2.6s (36.9%)

simplify48.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series182.0ms (2.6%)

rewrite51.0ms (0.7%)

simplify205.0ms (2.9%)

prune317.0ms (4.5%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify93.0ms (1.3%)

prune15.0ms (0.2%)

localize5.0ms (0.1%)

series20.0ms (0.3%)

rewrite10.0ms (0.1%)

simplify90.0ms (1.3%)

prune40.0ms (0.6%)

localize16.0ms (0.2%)

series501.0ms (7.2%)

rewrite104.0ms (1.5%)

simplify498.0ms (7.1%)

prune533.0ms (7.6%)

regimes279.0ms (4%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end74.0ms (1.1%)

Profiling