Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	48×	body	1280	valid
4.0ms	52×	body	640	valid
3.0ms	134×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	8×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
2.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

963×	`*-un-lft-identity`
724×	`times-frac`
575×	`add-sqr-sqrt`
468×	`prod-diff`
409×	`add-cube-cbrt`
185×	`distribute-lft-out`
92×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
46×	`div-inv`
28×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
5×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub`

Counts

2 → 561

Calls

2 calls:

10.0ms	(/ (+ x 1.0) (- x 1.0))
73.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series166.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (+ x 1.0) (- x 1.0))
128.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify191.0ms

Algorithm

egg-herbie

Counts

567 → 567

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1161	18191
1	3350	13265
2	5002	13161

prune692.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
2.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

356×	`*-un-lft-identity`
220×	`times-frac`
160×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
76×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-exp-log` `add-cbrt-cube`
21×	`difference-of-squares`
18×	`pow1` `fma-def` `associate-/r/`
9×	`frac-sub` `div-inv`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
6×	`flip3-+` `flip-+`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sub-neg` `fma-neg` `diff-log` `prod-diff` `frac-add` `sum-log`

Counts

4 → 287

Calls

4 calls:

50.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
31.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
47.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
52.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
205.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1192	2826
1	5001	2626

prune472.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 6.0 (/ 1 x))
0.5b	(/ 1 (pow x 2))
0.9b	(/ 1 (pow x 3))
9.0b	(+ (* 5.0 (/ 1 (pow x 2))) (+ (* 6.0 (/ 1 x)) (* 16.0 (/ 1 (pow x 3)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
61×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
54×	`add-cube-cbrt`
31×	`add-exp-log`
24×	`unpow-prod-down`
20×	`frac-add` `associate-/r*`
15×	`associate-*r/` `un-div-inv`
14×	`div-exp`
13×	`associate-r` `add-cbrt-cube`
12×	`cube-prod`
9×	`add-log-exp`
8×	`sqr-pow`
7×	`rec-exp` `1-exp`
6×	`pow1` `pow-to-exp` `pow-exp` `associate-/l*`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `prod-exp` `log1p-expm1-u` `unpow2`
3×	`cbrt-undiv` `flip3-+` `associate-l` `sum-log` `flip-+` `div-inv` `unswap-sqr`
2×	`pow-flip` `frac-2neg` `clear-num` `cbrt-unprod` `inv-pow`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `*-commutative`

Counts

4 → 200

Calls

4 calls:

7.0ms	(* 6.0 (/ 1 x))
4.0ms	(/ 1 (pow x 2))
4.0ms	(/ 1 (pow x 3))
19.0ms	(+ (* 5.0 (/ 1 (pow x 2))) (+ (* 6.0 (/ 1 x)) (* 16.0 (/ 1 (pow x 3)))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* 6.0 (/ 1 x))
16.0ms	(/ 1 (pow x 2))
36.0ms	(/ 1 (pow x 3))
28.0ms	(+ (* 5.0 (/ 1 (pow x 2))) (+ (* 6.0 (/ 1 x)) (* 16.0 (/ 1 (pow x 3)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	759	1186
1	4166	911
2	5001	883

prune443.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 5.0 (/ 1 (pow x 2)))
0.5b	(/ 1 (pow x 2))
0.9b	(/ 1 (pow x 3))
9.0b	(+ (* 5.0 (/ 1 (pow x 2))) (+ (pow (/ 6.0 x) 1) (* 16.0 (/ 1 (pow x 3)))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
80×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
62×	`add-cube-cbrt`
42×	`add-exp-log`
35×	`unpow-prod-down`
28×	`associate-r`
20×	`associate-/r*`
18×	`div-exp`
13×	`add-cbrt-cube` `sqr-pow`
12×	`cube-prod`
10×	`prod-exp`
9×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `unpow2` `add-log-exp` `unswap-sqr`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `frac-add` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3-+` `associate-r/` `associate-l*` `sum-log` `un-div-inv` `flip-+` `div-inv`
2×	`pow-flip` `frac-2neg` `clear-num` `cbrt-unprod` `inv-pow`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `*-commutative`

Counts

4 → 219

Calls

4 calls:

13.0ms	(* 5.0 (/ 1 (pow x 2)))
4.0ms	(/ 1 (pow x 2))
4.0ms	(/ 1 (pow x 3))
53.0ms	(+ (* 5.0 (/ 1 (pow x 2))) (+ (pow (/ 6.0 x) 1) (* 16.0 (/ 1 (pow x 3)))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 5.0 (/ 1 (pow x 2)))
15.0ms	(/ 1 (pow x 2))
35.0ms	(/ 1 (pow x 3))
29.0ms	(+ (* 5.0 (/ 1 (pow x 2))) (+ (pow (/ 6.0 x) 1) (* 16.0 (/ 1 (pow x 3)))))

simplify109.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	700	1284
1	3791	939
2	5001	911

prune503.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch112.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	18728.68752736968
10	-64880754058.88788	-2.651420353119469e-05	-15437.909064845162

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	38
1	62	38
2	72	38
3	73	38
4	73	38

end0.0ms

sample520.0ms

Algorithm

intervals

Results

176.0ms	1719×	body	1280	valid
103.0ms	1224×	body	640	valid
93.0ms	4124×	body	80	valid
37.0ms	618×	body	320	valid
17.0ms	315×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6