Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	203×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	19×	body	320	valid
1.0ms	8×	body	1280	valid
0.0ms	8×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.7b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`times-frac` `associate-l/` `associate-/r`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

10.0ms	(* (- 1.0 x) y)
9.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series139.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* (- 1.0 x) y)
64.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
44.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune139.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
2.7b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
18×	`add-sqr-sqrt` `associate-r`
13×	`times-frac`
11×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `add-log-exp`
3×	`flip3--` `flip--` `distribute-lft-out`
2×	`frac-times` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3-+` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 55

Calls

2 calls:

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

series108.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
67.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	362	398
1	1550	365
2	5001	365

prune114.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

2.7b	(- 1.0 (/ (* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0))) (+ 1.0 x)))
4.3b	(* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0)))
10.2b	(/ (* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0))) (+ 1.0 x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
18×	`associate-r`
17×	`add-exp-log` `times-frac` `add-cbrt-cube`
14×	`add-cube-cbrt`
5×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/` `distribute-lft-out` `add-log-exp`
4×	`frac-times` `associate-l` `associate-l/` `prod-exp` `associate-/r` `associate-/r/` `cbrt-unprod`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `distribute-lft-out--`

Counts

3 → 88

Calls

3 calls:

10.0ms	(- 1.0 (/ (* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0))) (+ 1.0 x)))
22.0ms	(* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0)))
13.0ms	(/ (* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0))) (+ 1.0 x))

series248.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- 1.0 (/ (* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0))) (+ 1.0 x)))
55.0ms	(* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0)))
64.0ms	(/ (* (- (* 1.0 1.0) (* x x)) (/ y (+ y 1.0))) (+ 1.0 x))

simplify85.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	575	965
1	2919	848
2	5001	847

prune197.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
0.0b	(- (/ 1 y) (/ x y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv` `distribute-lft-out--`
4×	`add-cube-cbrt` `associate-+l+`
3×	`sub-neg` `distribute-rgt-out--`
2×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
1×	`+-commutative` `flip3--` `flip3-+` `diff-log` `sum-log` `frac-sub` `flip--` `flip-+` `sub-div`

Counts

2 → 43

Calls

2 calls:

18.0ms	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
19.0ms	(- (/ 1 y) (/ x y))

series48.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
19.0ms	(- (/ 1 y) (/ x y))

simplify88.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	224	317
1	627	291
2	2889	282
3	5001	274

prune77.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes77.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.5b

bsearch78.0ms

Steps

Iters	Range		Point
8	11297247.164780367	8140883472.542182	325972206.36203164
10	-2.517375459137406e+24	-374005510135422.8	-378501471949656.7

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	29	10

end0.0ms

sample431.0ms

Algorithm

intervals

Results

145.0ms	6069×	body	80	valid
74.0ms	756×	body	640	valid
41.0ms	382×	body	1280	valid
31.0ms	495×	body	320	valid
13.0ms	298×	body	160	valid