Details

analyze886.0ms (10.4%)

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
0%	99.8%	0.2%	7
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	22×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify103.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

3.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.6b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	4.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	3.9b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series71.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

40.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
19.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
12.0ms	(/.f64 2 (-.f64 y t))

rewrite58.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 234

Calls

3 calls:

17.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
9.0ms	(/.f64 2 (-.f64 y t))
7.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)

simplify211.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
216×	`times-frac_binary64`
212×	`*-commutative_binary64`

Counts

342 → 351

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	7256
1	1123	6896
2	3980	6860
3	4623	6847
4	4989	6847

prune365.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	342	9	351
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	342	11	353

Error

Counts

353 → 11

Alt Table

Status	Error	Program
	4.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	4.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
▶	1.7b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	4.6b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	4.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	4.6b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
	4.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	4.9b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	28.9b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	4.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 7760 to 3652 computations (52.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.5b	(cbrt.f64 (-.f64 y t))
✓	0.6b	(cbrt.f64 z)
✓	1.2b	(/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))))

series1.5s (18%)

Counts

4 → 96

Calls

4 calls:

1.4s	(/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))))
49.0ms	(cbrt.f64 z)
41.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
31.0ms	(cbrt.f64 (-.f64 y t))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`cbrt-prod_binary64`
24×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 109

Calls

4 calls:

16.0ms	(/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
2.0ms	(cbrt.f64 (-.f64 y t))
1.0ms	(cbrt.f64 z)

simplify129.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

441×	`associate-r_binary64`
416×	`associate-l_binary64`
316×	`associate-/r*_binary64`
291×	`*-commutative_binary64`
218×	`fma-def_binary64`

Counts

205 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	451	5674
1	1228	4896
2	4641	4712
3	4972	4712

prune382.0ms (4.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	372	11	383

Error

Counts

383 → 11

Alt Table

Status	Error	Program
	4.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	4.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
✓	1.7b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	4.6b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	4.6b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
	4.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	4.9b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
▶	4.4b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	28.9b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	4.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 15699 to 6784 computations (56.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
	0.5b	(cbrt.f64 (-.f64 y t))
	0.6b	(cbrt.f64 z)
✓	3.7b	(/.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))

series1.4s (16.2%)

Counts

1 → 48

Calls

1 calls:

1.4s	(/.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
13×	`times-frac_binary64`
12×	`cbrt-div_binary64`
12×	`add-cbrt-cube_binary64`
10×	`cbrt-undiv_binary64`

Counts

1 → 48

Calls

1 calls:

14.0ms

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

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary64`
604×	`associate-/l/_binary64`
206×	`associate-r_binary64`
197×	`times-frac_binary64`
179×	`associate-/r*_binary64`

Counts

96 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	4276
1	901	3677
2	2912	3487
3	5462	3487

prune345.0ms (4.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	372	0	372
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	372	11	383

Error

Counts

383 → 11

Alt Table

Status	Error	Program
	4.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	4.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
✓	1.7b	(.f64 (/.f64 x (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	4.6b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	4.6b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
	4.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	4.9b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
✓	4.4b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	28.9b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
▶	4.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 15641 to 6575 computations (58% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 2 (cbrt.f64 (-.f64 y t)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
	0.5b	(cbrt.f64 (-.f64 y t))
✓	3.9b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

series133.0ms (1.6%)

Counts

3 → 96

Calls

3 calls:

49.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
44.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))
40.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))

rewrite101.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

203×	`times-frac_binary64`
174×	`add-sqr-sqrt_binary64`
146×	`*-un-lft-identity_binary64`
106×	`add-cube-cbrt_binary64`
102×	`associate-r_binary64`

Counts

3 → 258

Calls

3 calls:

46.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
9.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
5.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))

simplify219.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-*r/_binary64`
435×	`associate-*l/_binary64`
402×	`associate-/l*_binary64`
350×	`associate-/r*_binary64`
334×	`times-frac_binary64`

Counts

354 → 402

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	576	10935
1	1699	9691
2	5417	9691

prune507.0ms (5.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	551	1	552
Fresh	1	6	7
Picked	0	1	1
Done	1	2	3
Total	553	10	563

Error

Counts

563 → 10

Alt Table

Status	Error	Program
	4.8b	(/.f64 (/.f64 (*.f64 x 2) (-.f64 y t)) z)
	4.9b	(.f64 (.f64 x (/.f64 2 (-.f64 y t))) (/.f64 1 z))
	4.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z)))) (cbrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	4.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	4.6b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	4.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))
	4.8b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
✓	4.4b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (cbrt.f64 z)))
	28.9b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
✓	4.5b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 19033 to 7610 computations (60% saved)

regimes1.0s (12.2%)

Accuracy

Total 1.8b remaining (99.1%)

Threshold costs 0b (0%)

Counts

139 → 1

Compiler

Compiled 24219 to 14868 computations (38.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	25	46
2	29	46
3	31	46
4	32	46
5	31	46

end1.0ms (0%)

Compiler: Compiled 33 to 17 computations (48.5% saved)

sample832.0ms (9.8%)

Algorithm

1×

intervals

Results

371.0ms	8000×	body	128	valid
30.0ms	673×	body	128	invalid

Compiler

Compiled 266 to 162 computations (39.1% saved)

Details

analyze886.0ms (10.4%)

sample23.0ms (0.3%)

simplify103.0ms (1.2%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series71.0ms (0.8%)

rewrite58.0ms (0.7%)

simplify211.0ms (2.5%)

prune365.0ms (4.3%)

localize13.0ms (0.2%)

series1.5s (18%)

rewrite31.0ms (0.4%)

simplify129.0ms (1.5%)

prune382.0ms (4.5%)

localize16.0ms (0.2%)

series1.4s (16.2%)

rewrite19.0ms (0.2%)

simplify99.0ms (1.2%)

prune345.0ms (4.1%)

localize13.0ms (0.1%)

series133.0ms (1.6%)

rewrite101.0ms (1.2%)

simplify219.0ms (2.6%)

prune507.0ms (5.9%)

regimes1.0s (12.2%)

simplify4.0ms (0%)

end1.0ms (0%)

sample832.0ms (9.8%)

Profiling