Details

analyze1.3s (18.9%)

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)

sample2.7s (39.9%)

Results

1.0s	6355×	body	128	valid
704.0ms	971×	body	1024	valid
258.0ms	578×	body	512	valid
251.0ms	1580×	body	128	invalid
144.0ms	195×	body	1024	invalid
105.0ms	348×	body	256	valid
97.0ms	217×	body	512	invalid
50.0ms	152×	body	256	invalid
4.0ms	4×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify49.0ms (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

5.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.2b	(+.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	5.6b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series146.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

101.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
32.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
12.0ms	(/.f64 y (+.f64 y z))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`unpow-prod-down_binary64`

Counts

3 → 87

Calls

3 calls:

20.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
5.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
4.0ms	(/.f64 y (+.f64 y z))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

310×	`fma-def_binary64`
259×	`times-frac_binary64`
255×	`associate-+r+_binary64`
246×	`associate-r_binary64`
205×	`associate-+l+_binary64`

Counts

171 → 225

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	5061
1	1307	4883
2	5052	4883

prune150.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	222	3	225
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	223	3	226

Error

Counts

226 → 3

Alt Table

Status	Error	Program
	10.8b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	3.0b	(+.f64 x (/.f64 1 y))
	39.0b	(cbrt.f64 (.f64 (.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

Compiler

Compiled 6603 to 2877 computations (56.4% saved)

localize3.0ms (0%)

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))

simplify97.0ms (1.4%)

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

prune18.0ms (0.3%)

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

Counts

31 → 3

Alt Table

Status	Error	Program
▶	10.8b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.0b	(+.f64 x (/.f64 1 y))
	39.0b	(cbrt.f64 (.f64 (.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

Compiler

Compiled 398 to 238 computations (40.2% 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)

series24.0ms (0.4%)

Counts

2 → 44

Calls

2 calls:

17.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
7.0ms	(/.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))
3.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

simplify94.0ms (1.4%)

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

prune42.0ms (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

Counts

84 → 3

Alt Table

Status	Error	Program
✓	10.8b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.0b	(+.f64 x (/.f64 1 y))
▶	39.0b	(cbrt.f64 (.f64 (.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

Compiler

Compiled 1211 to 398 computations (67.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))
✓	0.1b	(*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))
	5.6b	(pow.f64 (/.f64 y (+.f64 y z)) y)
✓	36.7b	(cbrt.f64 (.f64 (.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

series429.0ms (6.3%)

Counts

3 → 108

Calls

3 calls:

185.0ms

(*.f64 (*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

138.0ms

(cbrt.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

105.0ms

(*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

rewrite189.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip-+_binary64`
60×	`frac-times_binary64`
60×	`flip3-+_binary64`
30×	`associate-*l/_binary64`
29×	`pow1_binary64`

Counts

3 → 140

Calls

3 calls:

63.0ms

(cbrt.f64 (*.f64 (*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

55.0ms

(*.f64 (*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

40.0ms

(*.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

simplify256.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

319×	`*-commutative_binary64`
313×	`+-commutative_binary64`
250×	`distribute-rgt-in_binary64`
245×	`distribute-lft-in_binary64`
243×	`associate-+r+_binary64`

Counts

248 → 325

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1012	20112
1	3312	18069
2	5219	18069

prune465.0ms (6.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	598	0	598
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	598	3	601

Error

Counts

601 → 3

Alt Table

Status	Error	Program
✓	10.8b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.0b	(+.f64 x (/.f64 1 y))
✓	39.0b	(cbrt.f64 (.f64 (.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))

Compiler

Compiled 40014 to 12045 computations (69.9% saved)

regimes579.0ms (8.5%)

Accuracy

Total 0.8b remaining (97.8%)

Threshold costs 0.8b (97.8%)

Counts

66 → 2

Compiler

Compiled 7519 to 4083 computations (45.7% saved)

bsearch36.0ms (0.5%)

Steps

Iters	Range		Point
8	5.166850437728975e-6	0.0032669810755203976	0.0032314348281543754

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (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	15	24
1	22	24
2	24	24
3	25	24
4	24	24

end58.0ms (0.8%)

Compiler: Compiled 95 to 50 computations (47.4% saved)

Details

analyze1.3s (18.9%)

sample2.7s (39.9%)

simplify49.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series146.0ms (2.1%)

rewrite33.0ms (0.5%)

simplify100.0ms (1.5%)

prune150.0ms (2.2%)

localize3.0ms (0%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify97.0ms (1.4%)

prune18.0ms (0.3%)

localize5.0ms (0.1%)

series24.0ms (0.4%)

rewrite10.0ms (0.1%)

simplify94.0ms (1.4%)

prune42.0ms (0.6%)

localize12.0ms (0.2%)

series429.0ms (6.3%)

rewrite189.0ms (2.8%)

simplify256.0ms (3.7%)

prune465.0ms (6.8%)

regimes579.0ms (8.5%)

bsearch36.0ms (0.5%)

simplify2.0ms (0%)

end58.0ms (0.8%)

Profiling