Details

sample20.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	18×	body	320	valid
0.0ms	8×	body	160	valid

simplify67.0ms

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: 19.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
1.7b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
5.2b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite63.0ms

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:

22.0ms	(* (- 1.0 x) y)
17.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
22.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series146.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* (- 1.0 x) y)
71.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
44.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (11.0ms)

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

prune142.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ (- 1.0 x) (/ (+ y 1.0) y))
1.7b	(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

167×	`times-frac`
157×	`*-un-lft-identity`
120×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
22×	`distribute-lft-out`
20×	`difference-of-squares`
19×	`associate-/r*`
18×	`distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1`
2×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `associate-/r/` `flip-+` `associate--r-`

Counts

3 → 169

Calls

3 calls:

19.0ms	(/ (+ y 1.0) y)
25.0ms	(/ (- 1.0 x) (/ (+ y 1.0) y))
50.0ms	(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (+ y 1.0) y)
44.0ms	(/ (- 1.0 x) (/ (+ y 1.0) y))
74.0ms	(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

simplify71.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	689	1514
1	2646	1460
2	5002	1460

prune308.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
4.1b	(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
9.8b	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
14.1b	(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
18×	`add-exp-log` `times-frac` `add-cbrt-cube`
15×	`associate-l` `distribute-lft-out`
12×	`unpow-prod-down` `cube-prod`
11×	`add-sqr-sqrt` `add-log-exp`
9×	`add-cube-cbrt` `associate-/r*`
6×	`pow1`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`cbrt-undiv` `div-exp` `associate-/r/`
3×	`associate-r` `associate-*l/` `sum-cubes`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+r+` `flip3--` `distribute-lft-in` `diff-log` `associate-*r/` `sum-log` `flip--` `div-inv` `associate-/l/` `associate--r+`
1×	`+-commutative` `associate-+r-` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

18.0ms	(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
5.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
46.0ms	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
149.0ms	(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (* y y) (- (* 1.0 1.0) (* y 1.0)))
248.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0)))))
94.0ms	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
112.0ms	(* (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))) (+ (* y y) (- (* 1.0 1.0) (* y 1.0))))

simplify96.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	645	1335
1	3576	1152
2	5001	1147

prune318.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

9.8b	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
9.8b	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
10.5b	(* (- (* 1.0 1.0) (* y 1.0)) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
14.4b	(* (* y y) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity`
44×	`add-exp-log` `add-cbrt-cube`
36×	`times-frac`
30×	`associate-r` `distribute-lft-out`
24×	`unpow-prod-down` `cube-prod`
18×	`associate-/r*`
17×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
8×	`associate-/r/`
6×	`associate-*l/` `sum-cubes`
5×	`associate-l`
4×	`flip3--` `flip3-+` `pow-prod-down` `flip--` `flip-+` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative` `associate-/l*` `unswap-sqr`
1×	`distribute-rgt-out--`

Counts

4 → 154

Calls

4 calls:

46.0ms	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
46.0ms	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
104.0ms	(* (- (* 1.0 1.0) (* y 1.0)) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
100.0ms	(* (* y y) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
94.0ms	(/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3)))
73.0ms	(* (- (* 1.0 1.0) (* y 1.0)) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))
75.0ms	(* (* y y) (/ (* (- 1.0 x) y) (+ (pow y 3) (pow 1.0 3))))

simplify99.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	663	1554
1	3743	1253
2	5001	1253

prune420.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 14.4b

bsearch126.0ms

Steps

Iters	Range		Point
10	3473512885.6839814	1.134459934099945e+21	3406145480945.993
10	-8.115669647949308e+25	-40742292820.96068	-340993515449.59576

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	28
1	55	28

end0.0ms

sample461.0ms

Algorithm

intervals

Results

147.0ms	6097×	body	80	valid
66.0ms	769×	body	640	valid
38.0ms	366×	body	1280	valid
31.0ms	495×	body	320	valid
12.0ms	273×	body	160	valid