Details

sample51.0ms

Algorithm

intervals

Results

32.0ms

727×

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: 8.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
8.0b	(/ (* (cosh x) (/ y x)) z)

rewrite14.0ms

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)

series189.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (cosh x) (/ y x))
115.0ms	(/ (* (cosh x) (/ y x)) z)

simplify51.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (11.0ms)

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

prune146.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (cosh x) (/ y (* x z)))
5.6b	(/ y (* x z))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

9.0ms	(* (cosh x) (/ y (* x z)))
3.0ms	(/ y (* x z))

series132.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(* (cosh x) (/ y (* x z)))
21.0ms	(/ y (* x z))

simplify36.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	259	290
1	1062	239
2	5002	239

prune114.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.6b	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (* z x) y))
5.6b	(/ (* z x) y)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
16×	`times-frac`
12×	`cbrt-undiv` `div-exp`
11×	`*-un-lft-identity`
10×	`associate-/r*`
9×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-exp` `cbrt-unprod`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`frac-2neg` `flip3-+` `associate-r/` `clear-num` `flip-+` `associate-/l/` `associate-/l`
1×	`+-commutative` `sum-log` `associate-/r/` `distribute-lft-out`

Counts

3 → 73

Calls

3 calls:

4.0ms	(+ (exp (* -1 x)) (exp x))
9.0ms	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (* z x) y))
3.0ms	(/ (* z x) y)

series144.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (exp (* -1 x)) (exp x))
105.0ms	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (* z x) y))
18.0ms	(/ (* z x) y)

simplify61.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	441	684
1	2493	546
2	5001	546

prune208.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (/ (* z x) (* (cbrt y) (cbrt y))) (cbrt y)))
1.4b	(/ (/ (* z x) (* (cbrt y) (cbrt y))) (cbrt y))
4.4b	(/ (* z x) (* (cbrt y) (cbrt y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
90×	`add-exp-log`
59×	`add-cbrt-cube`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
51×	`cbrt-prod`
43×	`cbrt-undiv` `div-exp`
41×	`associate-/r*`
24×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
7×	`associate-/l*`
4×	`pow1` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`associate-*r/`
1×	`flip3-+` `pow1/3` `associate-/r/` `flip-+`

Counts

4 → 200

Calls

4 calls:

0.0ms	(cbrt y)
17.0ms	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (/ (* z x) (* (cbrt y) (cbrt y))) (cbrt y)))
9.0ms	(/ (/ (* z x) (* (cbrt y) (cbrt y))) (cbrt y))
5.0ms	(/ (* z x) (* (cbrt y) (cbrt y)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt y)
144.0ms	(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (/ (* z x) (* (cbrt y) (cbrt y))) (cbrt y)))
42.0ms	(/ (/ (* z x) (* (cbrt y) (cbrt y))) (cbrt y))
122.0ms	(/ (* z x) (* (cbrt y) (cbrt y)))

simplify56.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	932	2866
1	5001	2338

prune635.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes130.0ms

Accuracy

96.3% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 7.2b

bsearch79.0ms

Steps

Iters	Range		Point
8	6.907683956539121e-12	6.5383237107547055e-09	1.6175364036447777e-11
4	-6.5540093835560985e-15	-3.45304144449549e-15	-6.253949367303072e-15

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	20
1	35	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s

22409×

body

valid