Details

analyze1.4s (23.4%)

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)

sample2.4s (41.5%)

Results

935.0ms	6393×	body	128	valid
592.0ms	954×	body	1024	valid
279.0ms	600×	body	512	valid
199.0ms	1489×	body	128	invalid
109.0ms	187×	body	1024	invalid
93.0ms	220×	body	512	invalid
81.0ms	306×	body	256	valid
36.0ms	139×	body	256	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify47.0ms (0.8%)

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

6.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.0b	(+.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))
✓	5.4b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series186.0ms (3.2%)

Counts

4 → 108

Calls

4 calls:

99.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
44.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
32.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
10.0ms	(/.f64 y (+.f64 y z))

rewrite53.0ms (0.9%)

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:

15.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
10.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
6.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
3.0ms	(/.f64 y (+.f64 y z))

simplify193.0ms (3.3%)

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

prune321.0ms (5.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	426	4	430
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	427	4	431

Error

0.0b

Counts

431 → 4

Alt Table

Status	Error	Program
	6.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))
	36.0b	(+.f64 x (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) y) (pow.f64 (/.f64 (cbrt.f64 y) (+.f64 z y)) y)) y))
	8.4b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	2.4b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 12609 to 4741 computations (62.4% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(+.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 (1.6%)

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

prune36.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

0.0b

Counts

32 → 4

Alt Table

Status	Error	Program
▶	6.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))
	36.0b	(+.f64 x (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) y) (pow.f64 (/.f64 (cbrt.f64 y) (+.f64 z y)) y)) y))
	8.4b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.4b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 412 to 266 computations (35.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	5.4b	(pow.f64 (/.f64 y (+.f64 z y)) y)

series208.0ms (3.6%)

Counts

4 → 60

Calls

4 calls:

69.0ms	(cbrt.f64 y)
68.0ms	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
38.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
32.0ms	(pow.f64 (/.f64 y (+.f64 z y)) y)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/.f64 1 (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
5.0ms	(pow.f64 (/.f64 y (+.f64 z y)) y)
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify135.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

344×	`fma-neg_binary64`
267×	`associate-r_binary64`
228×	`times-frac_binary64`
199×	`sqr-pow_binary64`
193×	`associate-l_binary64`

Counts

187 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	344	3445
1	901	3113
2	3817	2942
3	4681	2907
4	4963	2907

prune175.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	239	4	243

Error

0.0b

Counts

243 → 4

Alt Table

Status	Error	Program
✓	6.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))
	16.6b	(+.f64 x (.f64 (pow.f64 (.f64 y y) -1/3) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))
▶	8.4b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.4b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 7287 to 2768 computations (62% 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)

series22.0ms (0.4%)

Counts

2 → 44

Calls

2 calls:

12.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
9.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

rewrite10.0ms (0.2%)

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)

simplify98.0ms (1.7%)

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

prune53.0ms (0.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	80	5	85

Error

Counts

85 → 5

Alt Table

Status	Error	Program
✓	6.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))
	16.6b	(+.f64 x (.f64 (pow.f64 (.f64 y y) -1/3) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))
	8.4b	(+.f64 x (/.f64 (/.f64 -1 (exp.f64 z)) (neg.f64 y)))
✓	8.4b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.4b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 1189 to 411 computations (65.4% saved)

regimes196.0ms (3.4%)

Accuracy

Total 0.9b remaining (98.4%)

Threshold costs 0.9b (98.4%)

Counts

23 → 2

Compiler

Compiled 2242 to 1317 computations (41.3% saved)

bsearch30.0ms (0.5%)

Steps

Iters	Range		Point
7	2.4679370586731477e-21	3.045367021601755e-19	2.9865184356591876e-19

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-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	17	27
1	23	27
2	25	27
3	26	27
4	25	27

end120.0ms (2.1%)

Compiler: Compiled 116 to 78 computations (32.8% saved)

Details

analyze1.4s (23.4%)

sample2.4s (41.5%)

simplify47.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series186.0ms (3.2%)

rewrite53.0ms (0.9%)

simplify193.0ms (3.3%)

prune321.0ms (5.5%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify93.0ms (1.6%)

prune36.0ms (0.6%)

localize15.0ms (0.3%)

series208.0ms (3.6%)

rewrite20.0ms (0.3%)

simplify135.0ms (2.3%)

prune175.0ms (3%)

localize5.0ms (0.1%)

series22.0ms (0.4%)

rewrite10.0ms (0.2%)

simplify98.0ms (1.7%)

prune53.0ms (0.9%)

regimes196.0ms (3.4%)

bsearch30.0ms (0.5%)

simplify3.0ms (0%)

end120.0ms (2.1%)

Profiling