Details

analyze917.0ms (10.8%)

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)

sample25.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	26×	body	128	invalid

Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify97.0ms (1.1%)

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

prune3.0ms (0%)

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

4.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.3b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 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)
✓	5.1b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series99.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

47.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
41.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
10.0ms	(/.f64 2 (-.f64 y t))

rewrite55.0ms (0.6%)

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:

16.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
7.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
4.0ms	(/.f64 2 (-.f64 y t))

simplify227.0ms (2.7%)

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

prune287.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	341	10	351
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	342	11	353

Error

0.0b

Counts

353 → 11

Alt Table

Status	Error	Program
▶	4.8b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
	25.8b	(.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (sqrt.f64 z))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) (sqrt.f64 z)))
	5.0b	(.f64 (.f64 x (/.f64 1 (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
	5.5b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	5.1b	(.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)))
	5.3b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	46.1b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (sqrt.f64 z)))
	24.7b	(.f64 x (.f64 (/.f64 2 (-.f64 (.f64 y y) (.f64 t t))) (/.f64 (+.f64 y t) z)))
✓	5.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	5.9b	(.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))))

Compiler

Compiled 7748 to 3652 computations (52.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 2 (cbrt.f64 (-.f64 y t)))
✓	0.5b	(cbrt.f64 (-.f64 y t))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
✓	4.0b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))

series162.0ms (1.9%)

Counts

4 → 120

Calls

4 calls:

48.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))
45.0ms	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
37.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
31.0ms	(cbrt.f64 (-.f64 y t))

rewrite101.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

203×	`times-frac_binary64`
178×	`add-sqr-sqrt_binary64`
150×	`*-un-lft-identity_binary64`
108×	`add-cube-cbrt_binary64`
102×	`associate-r_binary64`

Counts

4 → 275

Calls

4 calls:

45.0ms	(.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)))
4.0ms	(/.f64 2 (cbrt.f64 (-.f64 y t)))
2.0ms	(cbrt.f64 (-.f64 y t))

simplify206.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

437×	`associate-*l/_binary64`
417×	`associate-/l*_binary64`
373×	`associate-/r*_binary64`
348×	`times-frac_binary64`
257×	`fma-def_binary64`

Counts

395 → 453

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	11985
1	1964	10751
2	5274	10751

prune473.0ms (5.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	553	2	555
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	557	9	566

Error

Counts

566 → 9

Alt Table

Status	Error	Program
	5.5b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.4b	(.f64 (.f64 2 (/.f64 x (-.f64 y t))) (/.f64 1 z))
	5.3b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	4.8b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
▶	4.4b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t)))))) (/.f64 (/.f64 2 (cbrt.f64 (cbrt.f64 (-.f64 y t)))) (cbrt.f64 z)))
	24.7b	(.f64 x (.f64 (/.f64 2 (-.f64 (.f64 y y) (.f64 t t))) (/.f64 (+.f64 y t) z)))
✓	5.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	5.9b	(.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))))

Compiler

Compiled 19274 to 7713 computations (60% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t))))
✓	0.5b	(cbrt.f64 z)
✓	0.9b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t)))))) (/.f64 (/.f64 2 (cbrt.f64 (cbrt.f64 (-.f64 y t)))) (cbrt.f64 z)))
✓	2.6b	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t))))))

series1.7s (20.5%)

Counts

4 → 132

Calls

4 calls:

1.6s	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t))))))
70.0ms	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t)))))) (/.f64 (/.f64 2 (cbrt.f64 (cbrt.f64 (-.f64 y t)))) (cbrt.f64 z)))
46.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t))))
32.0ms	(cbrt.f64 z)

rewrite345.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

485×	`times-frac_binary64`
442×	`cbrt-prod_binary64`
381×	`add-exp-log_binary64`
323×	`add-sqr-sqrt_binary64`
279×	`*-un-lft-identity_binary64`

Counts

4 → 551

Calls

4 calls:

116.0ms	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t)))))) (/.f64 (/.f64 2 (cbrt.f64 (cbrt.f64 (-.f64 y t)))) (cbrt.f64 z)))
26.0ms	(/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t))))))
14.0ms	(*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t))))
1.0ms	(cbrt.f64 z)

simplify801.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

836×	`associate-/l*_binary64`
363×	`*-commutative_binary64`
297×	`fma-def_binary64`
228×	`associate-*r/_binary64`
215×	`associate-*l/_binary64`

Counts

683 → 850

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1004	42829
1	2899	34389
2	4923	34359
3	5003	34359

prune689.0ms (8.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	884	0	884
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	884	9	893

Error

Counts

893 → 9

Alt Table

Status	Error	Program
	5.5b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.4b	(.f64 (.f64 2 (/.f64 x (-.f64 y t))) (/.f64 1 z))
▶	5.3b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	4.8b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) z))
✓	4.4b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t)))))) (/.f64 (/.f64 2 (cbrt.f64 (cbrt.f64 (-.f64 y t)))) (cbrt.f64 z)))
	24.7b	(.f64 x (.f64 (/.f64 2 (-.f64 (.f64 y y) (.f64 t t))) (/.f64 (+.f64 y t) z)))
✓	5.2b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	5.9b	(.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))))

Compiler

Compiled 50485 to 11213 computations (77.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	0.0b	(*.f64 (-.f64 y t) z)
✓	5.3b	(/.f64 x (*.f64 (-.f64 y t) z))

series86.0ms (1%)

Counts

3 → 88

Calls

3 calls:

43.0ms	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
36.0ms	(/.f64 x (*.f64 (-.f64 y t) z))
7.0ms	(*.f64 (-.f64 y t) z)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 80

Calls

3 calls:

8.0ms	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
5.0ms	(/.f64 x (*.f64 (-.f64 y t) z))
4.0ms	(*.f64 (-.f64 y t) z)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

880×	`associate-/l*_binary64`
548×	`fma-def_binary64`
214×	`distribute-rgt-in_binary64`
180×	`associate-/r/_binary64`
159×	`distribute-lft-in_binary64`

Counts

168 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3209
1	493	2822
2	1977	2651
3	5468	2651

prune120.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	2	3	5
Picked	0	1	1
Done	2	1	3
Total	163	7	170

Error

Counts

170 → 7

Alt Table

Status	Error	Program
	5.5b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	6.3b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.4b	(.f64 (.f64 2 (/.f64 x (-.f64 y t))) (/.f64 1 z))
✓	5.3b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	4.4b	(.f64 (/.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 y t))) (cbrt.f64 (cbrt.f64 (-.f64 y t)))))) (/.f64 (/.f64 2 (cbrt.f64 (cbrt.f64 (-.f64 y t)))) (cbrt.f64 z)))
	7.0b	(*.f64 2 (/.f64 1 (/.f64 (-.f64 y t) (/.f64 x z))))
	6.4b	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 x z))

Compiler

Compiled 2844 to 1095 computations (61.5% saved)

regimes1.1s (13.1%)

Accuracy

Total 1.8b remaining (99%)

Threshold costs 0b (0%)

Counts

157 → 1

Compiler

Compiled 26139 to 15985 computations (38.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	24	46
2	28	46
3	30	46
4	31	46
5	30	46

end1.0ms (0%)

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

sample784.0ms (9.3%)

Algorithm

1×

intervals

Results

355.0ms	8000×	body	128	valid
32.0ms	702×	body	128	invalid

Compiler

Compiled 183 to 112 computations (38.8% saved)

Details

analyze917.0ms (10.8%)

sample25.0ms (0.3%)

simplify97.0ms (1.1%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series99.0ms (1.2%)

rewrite55.0ms (0.6%)

simplify227.0ms (2.7%)

prune287.0ms (3.4%)

localize10.0ms (0.1%)

series162.0ms (1.9%)

rewrite101.0ms (1.2%)

simplify206.0ms (2.4%)

prune473.0ms (5.6%)

localize16.0ms (0.2%)

series1.7s (20.5%)

rewrite345.0ms (4.1%)

simplify801.0ms (9.5%)

prune689.0ms (8.1%)

localize6.0ms (0.1%)

series86.0ms (1%)

rewrite21.0ms (0.3%)

simplify74.0ms (0.9%)

prune120.0ms (1.4%)

regimes1.1s (13.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample784.0ms (9.3%)

Profiling