Details

analyze26.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample17.0ms (0.8%)

Algorithm

1×

intervals

Results

5.0ms	68×	body	512	valid
4.0ms	153×	body	128	valid
1.0ms	26×	body	256	valid
1.0ms	9×	body	1024	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	25	13
4	32	13
5	48	13
6	70	13
7	79	13
8	91	13
9	93	13
10	87	13
11	73	13

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 30 to 24 computations (20% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
3.3b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

rewrite120.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

Rules

55×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
45×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
13×	`cancel-sign-sub-inv_binary64`

Counts

2 → 81

Calls

2 calls:

24.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
5.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 1218 to 980 computations (19.5% saved)

series40.0ms (2%)

Error

0.1b

Counts

2 → 23

Calls

2 calls:

13.0ms	(/.f64 1 (+.f64 x 1))
12.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 493 to 392 computations (20.5% saved)

simplify130.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

753×	`div-sub_binary64`
526×	`associate-*l/_binary64`
363×	`associate-/r*_binary64`
346×	`distribute-rgt-in_binary64`
274×	`distribute-lft-in_binary64`

Counts

104 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1503
1	274	1465
2	569	1441
3	1665	1429
4	4689	1429
5	4533	1429
6	4823	1429

prune35.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

0.1b

Counts

84 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 -1 (+.f64 x (*.f64 x x)))
✓	13.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	32.2b	(-.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))))

Compiler

Compiled 621 to 472 computations (24% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 x x))
0.1b	(/.f64 -1 (+.f64 x (*.f64 x x)))

rewrite65.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`distribute-rgt1-in_binary64` `distribute-rgt-out_binary64` `associate-/r*_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 -1 (+.f64 x (*.f64 x x)))
3.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 715 to 306 computations (57.2% saved)

series28.0ms (1.4%)

Error

0.1b

Counts

2 → 18

Calls

2 calls:

12.0ms	(/.f64 -1 (+.f64 x (*.f64 x x)))
10.0ms	(+.f64 x (*.f64 x x))

Compiler

Compiled 304 to 243 computations (20.1% saved)

simplify80.0ms (4%)

Algorithm

1×	egg-herbie

Rules

535×	`times-frac_binary64`
425×	`associate-/r*_binary64`
384×	`div-sub_binary64`
329×	`associate-/l/_binary64`
234×	`associate-/l*_binary64`

Counts

68 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	1031
1	214	968
2	513	966
3	1382	966
4	4263	966
5	5156	966

prune28.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	36	5	41

Error

0.0b

Counts

41 → 5

Alt Table

Status	Error	Program
	38.6b	(.f64 (/.f64 -1 (-.f64 (.f64 x x) (pow.f64 x 4))) (-.f64 x (*.f64 x x)))
	0.1b	(*.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1)))
▶	0.1b	(/.f64 1 (*.f64 x (-.f64 -1 x)))
	30.8b	(cbrt.f64 (pow.f64 (/.f64 -1 (+.f64 x (*.f64 x x))) 3))
✓	13.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

Compiler

Compiled 412 to 268 computations (35% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.1b	(/.f64 1 (*.f64 x (-.f64 -1 x)))

rewrite32.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`pow1_binary64` `div-exp_binary64`
3×	`prod-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `times-frac_binary64` `-un-lft-identity_binary64` `associate-/l_binary64`
2×	`pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64`

Counts

1 → 30

Calls

1 calls:

6.0ms

(/.f64 1 (*.f64 x (-.f64 -1 x)))

Compiler

Compiled 346 to 265 computations (23.4% saved)

series19.0ms (0.9%)

Error

0.0b

Counts

1 → 12

Calls

1 calls:

14.0ms

(/.f64 1 (*.f64 x (-.f64 -1 x)))

Compiler

Compiled 233 to 189 computations (18.9% saved)

simplify73.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

798×	`div-sub_binary64`
448×	`associate-/r*_binary64`
411×	`distribute-rgt-in_binary64`
382×	`distribute-lft-in_binary64` `associate-/l*_binary64`
324×	`associate-/l/_binary64`

Counts

42 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	567
1	161	504
2	435	499
3	1284	498
4	4309	498
5	5812	498

prune16.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	31	4	35

Error

0.0b

Counts

35 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1)))
✓	0.1b	(/.f64 1 (*.f64 x (-.f64 -1 x)))
✓	13.4b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
	3.5b	(*.f64 (/.f64 1 (-.f64 x (pow.f64 x 3))) (+.f64 -1 x))

Compiler

Compiled 233 to 169 computations (27.5% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 -1 (+.f64 x 1))
0.1b	(*.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1)))

rewrite115.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

43×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
26×	`add-exp-log_binary64` `add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 94

Calls

2 calls:

14.0ms	(*.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1)))
5.0ms	(/.f64 -1 (+.f64 x 1))

Compiler

Compiled 1476 to 1184 computations (19.8% saved)

series39.0ms (1.9%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

12.0ms	(*.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1)))
12.0ms	(/.f64 -1 (+.f64 x 1))

Compiler

Compiled 513 to 407 computations (20.7% saved)

simplify109.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

586×	`times-frac_binary64`
484×	`div-sub_binary64`
352×	`associate-/l*_binary64`
284×	`distribute-rgt-in_binary64`
273×	`associate-*l/_binary64`

Counts

118 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	151	1826
1	373	1635
2	1007	1633
3	2970	1626
4	4405	1626
5	5198	1626

prune66.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	86	7	93

Error

Counts

93 → 7

Alt Table

Status	Error	Program
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (/.f64 -1 (+.f64 x 1)) (cbrt.f64 x)))
	0.1b	(/.f64 1 (*.f64 x (-.f64 -1 x)))
	33.6b	(*.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (neg.f64 (sqrt.f64 (/.f64 1 x))) (+.f64 x 1)))
	33.6b	(*.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 -1 (+.f64 x 1)) (sqrt.f64 x)))
	1.0b	(.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (neg.f64 (cbrt.f64 (/.f64 1 x))) (+.f64 x 1)))
	0.1b	(/.f64 (/.f64 -1 x) (+.f64 x 1))
	3.5b	(*.f64 (/.f64 1 (-.f64 x (pow.f64 x 3))) (+.f64 -1 x))

Compiler

Compiled 913 to 679 computations (25.6% saved)

regimes290.0ms (14.3%)

Accuracy

Total 0.4b remaining (98.4%)

Threshold costs 0.4b (98.4%)

Compiler

Compiled 3824 to 2864 computations (25.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`sub-neg_binary64` `*-commutative_binary64` `+-commutative_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	10
2	15	10
3	17	10
4	18	10
5	17	10

end1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample657.0ms (32.5%)

Algorithm

1×

intervals

Results

149.0ms	1967×	body	512	valid
121.0ms	4656×	body	128	valid
51.0ms	977×	body	256	valid
37.0ms	400×	body	1024	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 114 to 86 computations (24.6% saved)

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	25	13
4	32	13
5	48	13
6	70	13
7	79	13
8	91	13
9	93	13
10	87	13
11	73	13

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	25	13
4	32	13
5	48	13
6	70	13
7	79	13
8	91	13
9	93	13
10	87	13
11	73	13

Details

analyze26.0ms (1.3%)

sample17.0ms (0.8%)

simplify11.0ms (0.5%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite120.0ms (5.9%)

series40.0ms (2%)

simplify130.0ms (6.4%)

prune35.0ms (1.7%)

localize4.0ms (0.2%)

rewrite65.0ms (3.2%)

series28.0ms (1.4%)

simplify80.0ms (4%)

prune28.0ms (1.4%)

localize4.0ms (0.2%)

rewrite32.0ms (1.6%)

series19.0ms (0.9%)

simplify73.0ms (3.6%)

prune16.0ms (0.8%)

localize8.0ms (0.4%)

rewrite115.0ms (5.7%)

series39.0ms (1.9%)

simplify109.0ms (5.4%)

prune66.0ms (3.3%)

regimes290.0ms (14.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample657.0ms (32.5%)

Profiling

Iter	Nodes	Cost
0	7	13
1	12	13
2	18	13
3	25	13
4	32	13
5	48	13
6	70	13
7	79	13
8	91	13
9	93	13
10	87	13
11	73	13