Details

sample41.0ms

Algorithm

intervals

Results

22.0ms

718×

body

valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 4.7b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
4.4b	(/ (* (cosh x) (/ y x)) z)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 60

Calls

2 calls:

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

series187.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(* (cosh x) (/ y x))
109.0ms	(/ (* (cosh x) (/ y x)) z)

simplify39.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	345	374
1	1456	317
2	5001	317

prune149.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.2b	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ x y))
4.4b	(/ (/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ x y)) z)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
70×	`*-un-lft-identity`
68×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/l*`
17×	`cbrt-undiv` `div-exp`
16×	`associate-/r*`
12×	`div-inv`
5×	`associate-/r/` `add-log-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `associate-/l/`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

3 → 156

Calls

3 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
10.0ms	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ x y))
14.0ms	(/ (/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ x y)) z)

series175.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (exp (* -1 x)) (exp x))
59.0ms	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ x y))
89.0ms	(/ (/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ x y)) z)

simplify101.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	856	1876
1	4026	1689
2	5003	1689

prune493.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(* y (+ (exp (* -1 x)) (exp x)))
0.3b	(* (/ 1/2 x) (* y (+ (exp (* -1 x)) (exp x))))
4.4b	(/ (* (/ 1/2 x) (* y (+ (exp (* -1 x)) (exp x)))) z)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
14.0ms	(* y (+ (exp (* -1 x)) (exp x)))
25.0ms	(* (/ 1/2 x) (* y (+ (exp (* -1 x)) (exp x))))
21.0ms	(/ (* (/ 1/2 x) (* y (+ (exp (* -1 x)) (exp x)))) z)

series210.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (exp (* -1 x)) (exp x))
43.0ms	(* y (+ (exp (* -1 x)) (exp x)))
58.0ms	(* (/ 1/2 x) (* y (+ (exp (* -1 x)) (exp x))))
88.0ms	(/ (* (/ 1/2 x) (* y (+ (exp (* -1 x)) (exp x)))) z)

simplify77.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	581	1111
1	3093	905
2	5002	905

prune294.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(* y (+ (exp (* -1 x)) (exp x)))
0.0b	(/ (* y (+ (exp (* -1 x)) (exp x))) x)
4.4b	(/ (* 1/2 (/ (* y (+ (exp (* -1 x)) (exp x))) x)) z)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`cbrt-undiv` `div-exp`
6×	`pow1` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
5×	`associate-*r/`
4×	`associate-r`
3×	`flip3-+` `associate-l` `flip-+` `associate-/l/`
2×	`frac-2neg` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
15.0ms	(* y (+ (exp (* -1 x)) (exp x)))
7.0ms	(/ (* y (+ (exp (* -1 x)) (exp x))) x)
16.0ms	(/ (* 1/2 (/ (* y (+ (exp (* -1 x)) (exp x))) x)) z)

series232.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (exp (* -1 x)) (exp x))
38.0ms	(* y (+ (exp (* -1 x)) (exp x)))
70.0ms	(/ (* y (+ (exp (* -1 x)) (exp x))) x)
98.0ms	(/ (* 1/2 (/ (* y (+ (exp (* -1 x)) (exp x))) x)) z)

simplify59.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	452	822
1	2368	672
2	5001	672

prune218.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

regimes118.0ms

Accuracy

91.2% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 7.6b

bsearch49.0ms

Steps

Iters	Range		Point
4	3823021508017.3535	6440083886036.53	4072403334666.2456
4	-8.270448809239973e-17	-4.7064517331606615e-17	-6.479430494909423e-17

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

604.0ms

22103×

body

valid