Details

Time bar (total: 18.8s)

sample67.0ms

Algorithm
intervals
Results
32.0ms775×body80valid

simplify6.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1188
2418
31028
42248
53778
65928
712288
834768
done50008

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(cosh x)
0.0b
(* (cosh x) (/ y x))
5.7b
(/ (* (cosh x) (/ y x)) z)

rewrite36.0ms

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)
19.0ms
(* (cosh x) (/ y x))
14.0ms
(/ (* (cosh x) (/ y x)) z)

series312.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(cosh x)
110.0ms
(* (cosh x) (/ y x))
137.0ms
(/ (* (cosh x) (/ y x)) z)

simplify1.4s

Counts
83 → 83
Iterations

Useful iterations: 2 (279.0ms)

IterNodesCost
0156811
1366770
21353665
done5000665

prune273.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (exp x) (exp (- x)))
0.0b
(* y (* 1/2 (+ (exp x) (exp (- x)))))
4.9b
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log add-cbrt-cube
12×prod-exp cbrt-unprod
8×pow1 associate-*r/
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×distribute-rgt-in distribute-lft-in
3×expm1-log1p-u fma-def flip3-+ associate-*l* pow-prod-down flip-+ log1p-expm1-u
2×associate-/l/
1×+-commutative frac-2neg times-frac associate-*r* clear-num associate-/r* sum-log *-commutative div-inv distribute-lft-out associate-/l*
Counts
3 → 72
Calls
3 calls:
14.0ms
(+ (exp x) (exp (- x)))
56.0ms
(* y (* 1/2 (+ (exp x) (exp (- x)))))
70.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

series200.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (exp x) (exp (- x)))
56.0ms
(* y (* 1/2 (+ (exp x) (exp (- x)))))
113.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

simplify1.2s

Counts
81 → 81
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01521252
14291186
22381934
done5001929

prune234.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

3.4b
(cbrt (/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x)))
4.9b
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))
4.9b
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))
4.9b
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log add-cbrt-cube
27×prod-exp cbrt-unprod
18×cbrt-undiv div-exp
12×associate-*r/
6×associate-/l/
5×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u times-frac log1p-expm1-u div-inv add-log-exp
3×frac-2neg flip3-+ clear-num associate-/r* flip-+ associate-/l*
1×cbrt-div pow1/3
Counts
4 → 103
Calls
4 calls:
41.0ms
(cbrt (/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x)))
96.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))
57.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))
81.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

series963.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(cbrt (/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x)))
397.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))
160.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))
135.0ms
(/ (* y (* 1/2 (+ (exp x) (exp (- x))))) (* z x))

simplify1.3s

Counts
115 → 115
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01582534
14302400
223051822
done50001809

prune433.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
0.6b
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
0.6b
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
4.9b
(/ (* (* (cbrt (* y (* 1/2 (+ (exp x) (exp (- x)))))) (cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))) (cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))) (* z x))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*r/
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×associate-/l/
25×add-exp-log
17×add-cbrt-cube
14×associate-*l/
9×prod-exp cbrt-unprod
6×cbrt-undiv div-exp
4×pow1 add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 92
Calls
4 calls:
45.0ms
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
50.0ms
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
41.0ms
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
110.0ms
(/ (* (* (cbrt (* y (* 1/2 (+ (exp x) (exp (- x)))))) (cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))) (cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))) (* z x))

series754.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
181.0ms
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
183.0ms
(cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))
201.0ms
(/ (* (* (cbrt (* y (* 1/2 (+ (exp x) (exp (- x)))))) (cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))) (cbrt (* y (* 1/2 (+ (exp x) (exp (- x))))))) (* z x))

simplify1.2s

Counts
104 → 104
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01713203
14712961
220081905
done50001703

prune699.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0b

regimes352.0ms

Accuracy

95.1% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 7.0b

bsearch133.0ms

Steps
ItersRangePoint
9
4.861077116233833e+20
6.6094121709703044e+25
1.8049362431750824e+23
7
-3.423602116682063e-37
-4.786244883458866e-39
-3.3781132449665854e-37

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02150
12937
done2937

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s22060×body80valid