Details

sample39.0ms

Algorithm

intervals

Results

21.0ms

737×

body

valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	4
1	41	4
2	102	4
3	224	4
4	401	4
5	758	4
6	2403	4
7	5002	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
6.3b	(/ (* (cosh x) (/ y x)) z)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-exp-log` `add-cbrt-cube`
13×	`add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-r*`
5×	`pow1` `cbrt-undiv` `cosh-def` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `associate-/l/` `add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

3 → 68

Calls

3 calls:

0.0ms	(cosh x)
7.0ms	(* (cosh x) (/ y x))
5.0ms	(/ (* (cosh x) (/ y x)) z)

series236.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(cosh x)
78.0ms	(* (cosh x) (/ y x))
112.0ms	(/ (* (cosh x) (/ y x)) z)

simplify47.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	372	414
1	1616	354
2	5001	354

prune166.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x))
6.3b	(/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x)) z)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log` `add-cbrt-cube`
32×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
16×	`associate-l`
13×	`cbrt-undiv` `div-exp` `associate-r`
8×	`prod-exp` `cbrt-unprod`
5×	`pow1` `add-log-exp`
4×	`distribute-lft-out` `unswap-sqr`
3×	`associate-/r*` `div-inv` `associate-/l/`
2×	`frac-times` `associate-r/` `associate-l/`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `associate-/l`

Counts

3 → 95

Calls

3 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
26.0ms	(* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x))
10.0ms	(/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x)) z)

series171.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (exp (* -1 x)) (exp x))
62.0ms	(* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x))
88.0ms	(/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x)) z)

simplify74.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	573	1021
1	2784	841
2	5001	841

prune244.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x))
6.4b	(* (* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x)) (/ 1 z))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
56×	`add-cbrt-cube`
40×	`prod-exp`
37×	`add-sqr-sqrt`
34×	`times-frac`
33×	`*-un-lft-identity`
30×	`div-exp`
26×	`associate-r`
25×	`add-cube-cbrt`
22×	`cbrt-unprod`
17×	`cbrt-undiv` `associate-l`
10×	`pow1`
6×	`frac-times` `associate-*l/`
5×	`rec-exp` `1-exp` `add-log-exp`
4×	`associate-*r/` `pow-prod-down` `distribute-lft-out` `unswap-sqr`
3×	`div-inv`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `un-div-inv` `flip-+`

Counts

3 → 127

Calls

3 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
24.0ms	(* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x))
33.0ms	(* (* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x)) (/ 1 z))

series173.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (exp (* -1 x)) (exp x))
60.0ms	(* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x))
89.0ms	(* (* (/ (+ (exp (* -1 x)) (exp x)) 2) (/ y x)) (/ 1 z))

simplify93.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	773	1455
1	4004	1164
2	5001	1151

prune277.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) y) z)
0.0b	(* (/ (+ (exp (* -1 x)) (exp x)) 2) y)
6.6b	(/ (/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) y) z) x)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
16×	`associate-l`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
7×	`div-inv`
6×	`pow1` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`distribute-lft-out`
3×	`associate-r`
2×	`frac-2neg` `associate-*l/` `clear-num` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 121

Calls

4 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
8.0ms	(/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) y) z)
19.0ms	(* (/ (+ (exp (* -1 x)) (exp x)) 2) y)
11.0ms	(/ (/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) y) z) x)

series234.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (exp (* -1 x)) (exp x))
70.0ms	(/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) y) z)
55.0ms	(* (/ (+ (exp (* -1 x)) (exp x)) 2) y)
89.0ms	(/ (/ (* (/ (+ (exp (* -1 x)) (exp x)) 2) y) z) x)

simplify71.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	575	1324
1	2698	1133
2	5002	1133

prune291.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

87% (0.9b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 6.8b

bsearch82.0ms

Steps

Iters	Range		Point
8	6.001376977234749e+25	2.022852572354262e+29	6.975907784848722e+25
8	-2.6245337278422527e+66	-1.4333731922804479e+62	-1.461823739049789e+62

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	14
1	37	14

end0.0ms

sample1.1s

Algorithm

intervals

Results

591.0ms

22530×

body

valid