Details

Time bar (total: 8.8s)

sample37.0ms

Algorithm
intervals
Results
20.0ms698×body80valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0184
1414
21024
32244
44014
57584
624034
750024

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(cosh x)
0.0b
(* (cosh x) (/ y x))
8.3b
(/ (* (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)

series237.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(cosh x)
78.0ms
(* (cosh x) (/ y x))
112.0ms
(/ (* (cosh x) (/ y x)) z)

simplify44.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0372414
11616354
25001354

prune169.0ms

Filtered
77 candidates to 59 candidates (76.6%)
Pruning

11 alts after pruning (10 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))
0.5b
(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (* z x) y))
8.1b
(/ (* z x) y)

rewrite23.0ms

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:
7.0ms
(+ (exp (* -1 x)) (exp x))
10.0ms
(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (* z x) y))
4.0ms
(/ (* z x) y)

series141.0ms

Counts
3 → 9
Calls
3 calls:
20.0ms
(+ (exp (* -1 x)) (exp x))
103.0ms
(/ (* 1/2 (+ (exp (* -1 x)) (exp x))) (/ (* z x) y))
18.0ms
(/ (* z x) y)

simplify59.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0441684
12493546
25001546

prune212.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ z (+ (exp (* -1 x)) (exp x)))
0.0b
(/ 1/2 (/ z (+ (exp (* -1 x)) (exp x))))
0.0b
(+ (exp (* -1 x)) (exp x))
7.1b
(/ (/ 1/2 (/ z (+ (exp (* -1 x)) (exp x)))) (/ x y))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
2681×times-frac
1372×*-un-lft-identity
1086×add-sqr-sqrt add-cube-cbrt
143×distribute-lft-out
123×div-inv
110×associate-/r/
65×associate-/l*
48×flip3-+ flip-+
35×associate-/r*
32×add-exp-log add-cbrt-cube
19×cbrt-undiv div-exp
6×add-log-exp
4×pow1
3×frac-2neg clear-num
1×+-commutative sum-log associate-/l/
Counts
4 → 998
Calls
4 calls:
7.0ms
(/ z (+ (exp (* -1 x)) (exp x)))
11.0ms
(/ 1/2 (/ z (+ (exp (* -1 x)) (exp x))))
4.0ms
(+ (exp (* -1 x)) (exp x))
46.0ms
(/ (/ 1/2 (/ z (+ (exp (* -1 x)) (exp x)))) (/ x y))

series259.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ z (+ (exp (* -1 x)) (exp x)))
60.0ms
(/ 1/2 (/ z (+ (exp (* -1 x)) (exp x))))
20.0ms
(+ (exp (* -1 x)) (exp x))
113.0ms
(/ (/ 1/2 (/ z (+ (exp (* -1 x)) (exp x)))) (/ x y))

simplify234.0ms

Algorithm
egg-herbie
Counts
1010 → 1010
Iterations

Useful iterations: 1 (71.0ms)

IterNodesCost
0483019430
1500119339

prune3.3s

Filtered
1010 candidates to 737 candidates (73.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ x y) 1/2) (- (+ (exp (+ (* -1 x) (* -1 x))) (exp (+ x x))) (exp (+ (* -1 x) x))))
0.1b
(pow (exp x) 3)
0.1b
(pow (exp (* -1 x)) 3)
7.1b
(/ (/ 1 (/ z (+ (pow (exp (* -1 x)) 3) (pow (exp x) 3)))) (* (/ (/ x y) 1/2) (- (+ (exp (+ (* -1 x) (* -1 x))) (exp (+ x x))) (exp (+ (* -1 x) x)))))

rewrite571.0ms

Algorithm
rewrite-expression-head
Rules
533×times-frac
378×*-un-lft-identity
204×add-sqr-sqrt
193×add-cube-cbrt
131×add-exp-log
104×associate-/l*
91×distribute-lft-out
80×div-exp
78×unpow-prod-down cube-prod
69×add-cbrt-cube
43×associate-*l*
36×cbrt-undiv
24×prod-exp
19×associate-/r/
18×sum-cubes
13×div-inv
12×cbrt-unprod
8×pow1 rec-exp 1-exp
7×pow-pow
6×pow-unpow flip3-+ associate-*r* flip-+
5×add-log-exp
4×frac-times exp-prod flip3-- associate-*r/ flip--
3×distribute-rgt-in distribute-lft-in unswap-sqr
2×cube-mult pow-to-exp sub-neg unpow3 associate-*l/ pow-exp associate--l+ distribute-lft-out-- rem-cube-cbrt sqr-pow
1×cube-div exp-neg exp-to-pow frac-2neg mul-1-neg pow-prod-down clear-num associate-/r* *-commutative associate-/l/ difference-of-squares
Counts
4 → 395
Calls
4 calls:
373.0ms
(* (/ (/ x y) 1/2) (- (+ (exp (+ (* -1 x) (* -1 x))) (exp (+ x x))) (exp (+ (* -1 x) x))))
2.0ms
(pow (exp x) 3)
2.0ms
(pow (exp (* -1 x)) 3)
164.0ms
(/ (/ 1 (/ z (+ (pow (exp (* -1 x)) 3) (pow (exp x) 3)))) (* (/ (/ x y) 1/2) (- (+ (exp (+ (* -1 x) (* -1 x))) (exp (+ x x))) (exp (+ (* -1 x) x)))))

series520.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ (/ x y) 1/2) (- (+ (exp (+ (* -1 x) (* -1 x))) (exp (+ x x))) (exp (+ (* -1 x) x))))
25.0ms
(pow (exp x) 3)
24.0ms
(pow (exp (* -1 x)) 3)
346.0ms
(/ (/ 1 (/ z (+ (pow (exp (* -1 x)) 3) (pow (exp x) 3)))) (* (/ (/ x y) 1/2) (- (+ (exp (+ (* -1 x) (* -1 x))) (exp (+ x x))) (exp (+ (* -1 x) x)))))

simplify114.0ms

Algorithm
egg-herbie
Counts
407 → 407
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
020579501
150018464

prune1.3s

Filtered
407 candidates to 202 candidates (49.6%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes259.0ms

Accuracy

95.6% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 7.4b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03619
13619

end0.0ms

sample1.0s

Algorithm
intervals
Results
581.0ms22168×body80valid