Details

analyze103.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample32.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	61×	body	1024	valid
9.0ms	136×	body	128	valid
4.0ms	33×	body	512	valid
2.0ms	20×	body	256	valid
1.0ms	6×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify91.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	30.2b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
4.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite265.0ms (6.7%)

Algorithm

1×	rewrite-expression-head

Error

29.6b

Rules

47×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`

Counts

3 → 144

Calls

3 calls:

18.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
17.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
13.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 3558 to 2629 computations (26.1% saved)

series47.0ms (1.2%)

Error

0.0b

Counts

3 → 36

Calls

3 calls:

11.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(/.f64 x (+.f64 x 1))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 930 to 740 computations (20.4% saved)

simplify116.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-neg_binary64`
336×	`cancel-sign-sub-inv_binary64`
245×	`log-prod_binary64`
201×	`distribute-rgt-neg-in_binary64`
175×	`distribute-lft-neg-in_binary64`

Counts

180 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2548
1	597	2426
2	2458	2370
3	4221	2366
4	4987	2366

prune90.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	3	122

Error

0.0b

Counts

122 → 3

Alt Table

Status	Error	Program
	31.1b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
▶	30.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))

Compiler

Compiled 2034 to 1465 computations (28% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
4.6b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
4.6b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
4.6b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))

rewrite302.0ms (7.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-cube-cbrt_binary64`
23×	`frac-sub_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`add-log-exp_binary64`
14×	`pow1_binary64`

Counts

4 → 179

Calls

4 calls:

20.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
18.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
17.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
13.0ms	(cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))

Compiler

Compiled 10192 to 7598 computations (25.5% saved)

series104.0ms (2.6%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

20.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
18.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
17.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
17.0ms	(cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))

Compiler

Compiled 3579 to 2772 computations (22.5% saved)

simplify194.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
422×	`associate-l_binary64`
410×	`fma-neg_binary64`
367×	`associate-r_binary64`
223×	`distribute-rgt-in_binary64`

Counts

224 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	4714
1	438	4530
2	1295	4084
3	4378	4012
4	4954	4012
5	4854	4012

prune96.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Error

0.0b

Counts

108 → 3

Alt Table

Status	Error	Program
▶	31.1b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
✓	30.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))

Compiler

Compiled 4336 to 3172 computations (26.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 3 (pow.f64 x 3))
0.3b	(/.f64 1 (*.f64 x x))
7.0b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
9.5b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

rewrite238.0ms (6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

53×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-log-exp_binary64`
18×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

4 → 194

Calls

4 calls:

20.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
15.0ms	(/.f64 3 (pow.f64 x 3))
14.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
14.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 5991 to 4379 computations (26.9% saved)

series40.0ms (1%)

Error

0.0b

Counts

4 → 22

Calls

4 calls:

12.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
9.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
6.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 804 to 659 computations (18% saved)

simplify159.0ms (4%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-neg_binary64`
265×	`times-frac_binary64`
199×	`associate-l_binary64`
194×	`associate-/r*_binary64`
180×	`associate-r_binary64`

Counts

216 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	3687
1	609	3359
2	2865	3168
3	4898	3168
4	4935	3168

prune81.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	121	4	125

Error

0.0b

Counts

125 → 4

Alt Table

Status	Error	Program
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
▶	31.1b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x)))))
	44.5b	(/.f64 (-.f64 (.f64 (+.f64 (/.f64 3 x) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (.f64 x x)))) (+.f64 (/.f64 3 x) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (.f64 x x))))) (pow.f64 (/.f64 1 (.f64 x x)) 4)) (+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 -3 x) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x))))))
✓	30.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))

Compiler

Compiled 2784 to 2024 computations (27.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (pow.f64 x 4))
0.3b	(/.f64 1 (*.f64 x x))
7.1b	(fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x)))
7.6b	(+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x))))

rewrite179.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

38×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`

Counts

4 → 180

Calls

4 calls:

14.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x))))
14.0ms	(/.f64 1 (pow.f64 x 4))
14.0ms	(/.f64 1 (*.f64 x x))
10.0ms	(fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 4020 to 2886 computations (28.2% saved)

series42.0ms (1.1%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

12.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x))))
11.0ms	(fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x)))
7.0ms	(/.f64 1 (*.f64 x x))
6.0ms	(/.f64 1 (pow.f64 x 4))

Compiler

Compiled 753 to 609 computations (19.1% saved)

simplify127.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-def_binary64`
437×	`fma-neg_binary64`
286×	`associate-/l*_binary64`
245×	`distribute-rgt-in_binary64`
244×	`associate-*l/_binary64`

Counts

199 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	2591
1	372	2394
2	1148	1873
3	4528	1873
4	4980	1873
5	4893	1873

prune98.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	128	4	132

Error

0.0b

Counts

132 → 4

Alt Table

Status	Error	Program
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	31.1b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (pow.f64 x 4)) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x)))))
	44.5b	(/.f64 (-.f64 (.f64 (+.f64 (/.f64 3 x) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (.f64 x x)))) (+.f64 (/.f64 3 x) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (.f64 x x))))) (pow.f64 (/.f64 1 (.f64 x x)) 4)) (+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 -3 x) (fma.f64 3 (pow.f64 x -3) (/.f64 1 (*.f64 x x))))))
	30.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))) (cbrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))

Compiler

Compiled 2265 to 1718 computations (24.2% saved)

regimes478.0ms (12%)

Accuracy

Total 0.1b remaining (78.4%)

Threshold costs 0.1b (78.4%)

Compiler

Compiled 7145 to 5321 computations (25.5% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	75
1	40	75
2	54	75
3	70	75
4	81	75
5	86	75
6	87	75
7	85	75

end3.0ms (0.1%)

Compiler: Compiled 51 to 39 computations (23.5% saved)

sample1.0s (25.9%)

Algorithm

1×

intervals

Results

321.0ms	2002×	body	1024	valid
181.0ms	4282×	body	128	valid
119.0ms	982×	body	512	valid
43.0ms	227×	body	2048	valid
43.0ms	507×	body	256	valid

Compiler

Compiled 205 to 150 computations (26.8% saved)

Details

analyze103.0ms (2.6%)

sample32.0ms (0.8%)

simplify91.0ms (2.3%)

prune1.0ms (0%)

localize7.0ms (0.2%)

rewrite265.0ms (6.7%)

series47.0ms (1.2%)

simplify116.0ms (2.9%)

prune90.0ms (2.3%)

localize14.0ms (0.3%)

rewrite302.0ms (7.6%)

series104.0ms (2.6%)

simplify194.0ms (4.9%)

prune96.0ms (2.4%)

localize12.0ms (0.3%)

rewrite238.0ms (6%)

series40.0ms (1%)

simplify159.0ms (4%)

prune81.0ms (2%)

localize12.0ms (0.3%)

rewrite179.0ms (4.5%)

series42.0ms (1.1%)

simplify127.0ms (3.2%)

prune98.0ms (2.5%)

regimes478.0ms (12%)

bsearch6.0ms (0.1%)

simplify6.0ms (0.1%)

end3.0ms (0.1%)

sample1.0s (25.9%)

Profiling