Details

sample15.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	26	5
3	29	5
4	30	5
5	30	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
6.4b	(/ y (+ 1.0 (/ (* x y) 2.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
54×	`add-cube-cbrt` `prod-diff`
49×	`times-frac`
13×	`distribute-lft-out`
8×	`associate-/r/`
4×	`add-exp-log` `flip3-+` `associate-/r*` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
3×	`fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `distribute-lft-out--`

Counts

2 → 109

Calls

2 calls:

20.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
10.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

series104.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(- x (/ y (+ 1.0 (/ (* x y) 2.0))))
71.0ms	(/ y (+ 1.0 (/ (* x y) 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	574	2548
1	2067	1795
2	5001	1637

prune151.0ms

Filtered

115 candidates to 57 candidates (49.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Merged error: 0.0b

Counts

116 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
3.3b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
6.7b	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
16.2b	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
55×	`times-frac`
42×	`prod-diff`
23×	`associate-+l+` `associate-+r+` `distribute-neg-in`
21×	`add-log-exp`
18×	`associate-r` `difference-of-squares`
14×	`distribute-lft-neg-in` `fma-def` `distribute-lft-out--`
13×	`add-exp-log` `add-cbrt-cube`
12×	`distribute-rgt-neg-in`
9×	`distribute-rgt-out` `flip3--` `flip--` `div-inv` `distribute-lft-out`
8×	`associate-/r*`
6×	`pow1` `sum-log` `associate-/r/` `associate-/l*`
5×	`diff-log` `associate-l`
4×	`expm1-log1p-u` `neg-mul-1` `neg-log` `frac-add` `log1p-expm1-u` `distribute-neg-frac`
3×	`cbrt-undiv` `distribute-lft1-in` `div-exp`
2×	`frac-times` `sub-neg` `frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `associate-+r-` `flip3-+` `associate-r/` `pow-prod-down` `-commutative` `flip-+`

Counts

4 → 220

Calls

4 calls:

5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
22.0ms	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
13.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
58.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
1.0ms	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
102.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))

simplify188.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (160.0ms)

Iter	Nodes	Cost
0	840	2715
1	4423	2133
2	5001	2104

prune662.0ms

Filtered

232 candidates to 181 candidates (78.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	232	3	235

Merged error: 0b

Counts

235 → 3

localize24.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
6.4b	(/ y (- 1.0 (/ (* x y) 2.0)))
6.7b	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
16.2b	(* (- 1.0 (/ (* x y) 2.0)) (/ 1 (/ (fma (/ y 2.0) x 1.0) (/ y (- 1.0 (/ (* x y) 2.0))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

585×	`times-frac`
375×	`*-un-lft-identity`
372×	`add-sqr-sqrt`
273×	`add-cube-cbrt`
209×	`associate-r`
45×	`distribute-lft-out--`
42×	`prod-diff` `difference-of-squares`
40×	`add-exp-log`
26×	`associate-/r/`
23×	`associate-+l+` `associate-+r+` `distribute-neg-in`
22×	`add-cbrt-cube`
21×	`div-inv` `add-log-exp`
17×	`flip3--` `div-exp` `flip--`
14×	`distribute-lft-neg-in` `fma-def`
12×	`distribute-rgt-neg-in`
10×	`prod-exp`
9×	`distribute-rgt-out` `associate-/r*` `distribute-lft-out`
8×	`cbrt-undiv`
7×	`unswap-sqr`
6×	`pow1` `sum-log` `associate-/l*`
5×	`diff-log` `associate-l`
4×	`expm1-log1p-u` `neg-mul-1` `neg-log` `frac-add` `cbrt-unprod` `log1p-expm1-u` `distribute-neg-frac`
3×	`rec-exp` `distribute-lft1-in` `1-exp`
2×	`frac-times` `sub-neg` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `neg-sub0` `associate-+l-` `associate-+r-` `flip3-+` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip-+`

Counts

4 → 431

Calls

4 calls:

5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
6.0ms	(/ y (- 1.0 (/ (* x y) 2.0)))
19.0ms	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
64.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ 1 (/ (fma (/ y 2.0) x 1.0) (/ y (- 1.0 (/ (* x y) 2.0))))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
69.0ms	(/ y (- 1.0 (/ (* x y) 2.0)))
1.0ms	(+ (- (- 1.0 (/ (* x y) 2.0))) (- 1.0 (/ (* x y) 2.0)))
53.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ 1 (/ (fma (/ y 2.0) x 1.0) (/ y (- 1.0 (/ (* x y) 2.0))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

443 → 443

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	2189	5751
1	5001	5251

prune1.6s

Filtered

443 candidates to 335 candidates (75.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	443	3	446

Merged error: 0b

Counts

446 → 3

localize28.0ms

Local error

Found 4 expressions with local error:

3.3b	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
6.7b	(- (- (* (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0)) (/ (* x y) 2.0)) (- 1.0 (/ (* x y) 2.0)))
16.2b	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))
52.7b	(fma (- (/ y 2.0)) (/ x 1) (* (/ y 2.0) (/ x 1)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
46×	`add-cube-cbrt`
43×	`prod-diff`
37×	`times-frac`
23×	`associate--r+`
18×	`associate-r`
16×	`add-log-exp`
12×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
9×	`flip3--` `associate--l+` `flip--`
8×	`diff-log`
7×	`distribute-lft-out--`
6×	`pow1` `div-inv`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `associate--r-`

Counts

4 → 166

Calls

4 calls:

5.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
21.0ms	(- (- (* (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0)) (/ (* x y) 2.0)) (- 1.0 (/ (* x y) 2.0)))
14.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))
1.0ms	(fma (- (/ y 2.0)) (/ x 1) (* (/ y 2.0) (/ x 1)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0))))
35.0ms	(- (- (* (* (cbrt 1.0) (cbrt 1.0)) (cbrt 1.0)) (/ (* x y) 2.0)) (- 1.0 (/ (* x y) 2.0)))
110.0ms	(* (- 1.0 (/ (* x y) 2.0)) (/ y (- (* 1.0 1.0) (* (/ (* x y) 2.0) (/ (* x y) 2.0)))))
32.0ms	(fma (- (/ y 2.0)) (/ x 1) (* (/ y 2.0) (/ x 1)))

simplify151.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	975	3092
1	4862	1839
2	5001	1839

prune698.0ms

Filtered

178 candidates to 126 candidates (70.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	178	3	181

Merged error: 0b

Counts

181 → 3

regimes57.0ms

Accuracy

90.7% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 8.4b

bsearch82.0ms

Steps

Iters	Range		Point
7	0.0014765281187882199	0.09117784756913819	0.08972597238176828
8	-2.9148937725967404e-17	-3.1158541889032954e-21	-2.843277202027643e-17

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	34
1	43	34

end0.0ms

sample338.0ms

Algorithm

intervals

Results

213.0ms	7998×	body	80	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid