Details

Time bar (total: 11.6s)

sample40.0ms

Algorithm
intervals
Results
20.0ms730×body80valid

simplify3.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
078
1188
2408
3998
42198
53758
66268
714778
835958
done50008

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(cosh x)
0.3b
(* (cosh x) (/ y x))
6.4b
(/ (* (cosh x) (/ y x)) z)

rewrite17.0ms

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×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u 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 → 74
Calls
3 calls:
1.0ms
(cosh x)
8.0ms
(* (cosh x) (/ y x))
6.0ms
(/ (* (cosh x) (/ y x)) z)

series302.0ms

Counts
3 → 9
Calls
3 calls:
61.0ms
(cosh x)
101.0ms
(* (cosh x) (/ y x))
140.0ms
(/ (* (cosh x) (/ y x)) z)

simplify802.0ms

Counts
83 → 83
Iterations

Useful iterations: done (800.0ms)

IterNodesCost
0156811
1379770
21405665
done5000653

prune244.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(cosh x)
0.3b
(* (cosh x) (/ y (* x z)))
4.7b
(/ y (* x z))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×associate-*r*
6×times-frac
5×pow1 prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×expm1-log1p-u cosh-def associate-*l* log1p-expm1-u associate-/l* add-log-exp
2×div-inv
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative unswap-sqr
Counts
3 → 64
Calls
3 calls:
1.0ms
(cosh x)
10.0ms
(* (cosh x) (/ y (* x z)))
3.0ms
(/ y (* x z))

series231.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(cosh x)
149.0ms
(* (cosh x) (/ y (* x z)))
26.0ms
(/ y (* x z))

simplify884.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
0122673
1292651
21064553
done5001553

prune203.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (+ (exp x) (exp (- x))) (/ y (* x z))) 2)
0.0b
(+ (exp x) (exp (- x)))
0.3b
(* (+ (exp x) (exp (- x))) (/ y (* x z)))
4.7b
(/ y (* x z))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
10×cbrt-undiv div-exp
9×times-frac prod-exp cbrt-unprod
7×associate-*r*
6×pow1 add-log-exp
5×flip3-+ flip-+ associate-/l/
4×expm1-log1p-u frac-times associate-*l* associate-*l/ associate-/r* log1p-expm1-u associate-/l*
3×fma-def div-inv
2×frac-2neg associate-*r/ clear-num distribute-lft-out
1×+-commutative pow-prod-down sum-log *-commutative unswap-sqr
Counts
4 → 106
Calls
4 calls:
14.0ms
(/ (* (+ (exp x) (exp (- x))) (/ y (* x z))) 2)
6.0ms
(+ (exp x) (exp (- x)))
28.0ms
(* (+ (exp x) (exp (- x))) (/ y (* x z)))
4.0ms
(/ y (* x z))

series292.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (* (+ (exp x) (exp (- x))) (/ y (* x z))) 2)
35.0ms
(+ (exp x) (exp (- x)))
113.0ms
(* (+ (exp x) (exp (- x))) (/ y (* x z)))
26.0ms
(/ y (* x z))

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: 2 (321.0ms)

IterNodesCost
01831682
15081607
221901313
done50001313

prune357.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (cosh x))
0.2b
(sqrt (cosh x))
0.3b
(* (sqrt (cosh x)) (* (sqrt (cosh x)) (/ y (* x z))))
4.7b
(/ y (* x z))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×pow1
10×add-cube-cbrt cosh-def *-un-lft-identity sqrt-div
9×prod-exp sqrt-prod cbrt-unprod
6×associate-*l*
5×frac-times associate-*r/
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×times-frac pow-prod-down associate-*l/ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*r* clear-num associate-/r* *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
1.0ms
(sqrt (cosh x))
1.0ms
(sqrt (cosh x))
28.0ms
(* (sqrt (cosh x)) (* (sqrt (cosh x)) (/ y (* x z))))
3.0ms
(/ y (* x z))

series322.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (cosh x))
78.0ms
(sqrt (cosh x))
138.0ms
(* (sqrt (cosh x)) (* (sqrt (cosh x)) (/ y (* x z))))
25.0ms
(/ y (* x z))

simplify985.0ms

Counts
101 → 101
Iterations

Useful iterations: 2 (144.0ms)

IterNodesCost
01491121
1365916
21178766
done5000766

prune273.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes198.0ms

Accuracy

94.8% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.1b

bsearch82.0ms

Steps
ItersRangePoint
5
5.809660952736369e-50
2.2603201977916295e-49
1.5395142672545628e-49
7
-131863331651.28616
-1737578713.048853
-27156977852.05674

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01842
12530
done2530

end0.0ms

sample1.1s

Algorithm
intervals
Results
640.0ms22594×body80valid