Details

Time bar (total: 55.0s)

sample123.0ms

Algorithm
intervals
Results
91.0ms115×body10240exit
19.0ms256×body80valid

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(/ (exp a) (+ (exp a) (exp b)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize20.0ms

Local error

Found 2 expressions with local error:

0.8b
(/ (exp a) (+ (exp a) (exp b)))
0.0b
(+ (exp a) (exp b))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
5×distribute-lft-out
4×associate-/r* add-cbrt-cube add-log-exp
3×add-exp-log associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+ insert-posit16
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp div-inv
Counts
2 → 47
Calls
2 calls:
Slowest
24.0ms
(+ (exp a) (exp b))
19.0ms
(/ (exp a) (+ (exp a) (exp b)))

series95.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
61.0ms
(/ (exp a) (+ (exp a) (exp b)))
34.0ms
(+ (exp a) (exp b))

simplify1.0s

Counts
42 → 53
Calls
42 calls:
Slowest
370.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
124.0ms
(+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))
51.0ms
(- (+ (* 1/4 a) 1/2) (* 1/4 b))
48.0ms
(/ (* (cbrt (exp a)) (cbrt (exp a))) (* (cbrt (+ (exp a) (exp b))) (cbrt (+ (exp a) (exp b)))))
35.0ms
(/ (* (cbrt (exp a)) (cbrt (exp a))) (sqrt (+ (exp a) (exp b))))

prune506.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (exp a) (+ (exp a) (exp b)))
0.0b
(+ (exp a) (exp b))
0.0b
(log (exp (/ (exp a) (+ (exp a) (exp b)))))
0.0b
(exp (/ (exp a) (+ (exp a) (exp b))))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
36×exp-prod times-frac
30×add-sqr-sqrt add-cube-cbrt
19×log-pow
11×distribute-lft-out
7×add-log-exp
6×add-cbrt-cube associate-/r/
5×pow1 add-exp-log
4×associate-/r* flip3-+ flip-+ insert-posit16
3×log-prod div-inv associate-/l*
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg div-exp rem-log-exp rem-exp-log
Counts
4 → 105
Calls
4 calls:
Slowest
39.0ms
(log (exp (/ (exp a) (+ (exp a) (exp b)))))
35.0ms
(/ (exp a) (+ (exp a) (exp b)))
25.0ms
(exp (/ (exp a) (+ (exp a) (exp b))))
15.0ms
(+ (exp a) (exp b))

series163.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
59.0ms
(exp (/ (exp a) (+ (exp a) (exp b))))
46.0ms
(/ (exp a) (+ (exp a) (exp b)))
38.0ms
(log (exp (/ (exp a) (+ (exp a) (exp b)))))
20.0ms
(+ (exp a) (exp b))

simplify2.8s

Counts
89 → 117
Calls
89 calls:
Slowest
743.0ms
(/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (exp a) (exp b)) (+ (exp a) (exp b))) (+ (exp a) (exp b))))
281.0ms
(exp (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))))
187.0ms
(- (+ (* 1/4 (* a (exp 1/2))) (exp 1/2)) (* 1/4 (* b (exp 1/2))))
124.0ms
(exp (/ (exp a) (- (* (exp a) (exp a)) (* (exp b) (exp b)))))
104.0ms
(exp (* (cbrt (/ (exp a) (+ (exp a) (exp b)))) (cbrt (/ (exp a) (+ (exp a) (exp b))))))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize65.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (* (exp b) (exp b)) (* (exp a) (exp b)))
1.0b
(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
0.7b
(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
0.4b
(* (exp a) (exp b))

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
106×*-un-lft-identity
55×times-frac
41×add-sqr-sqrt
36×associate-*l*
35×distribute-lft-out
34×add-cube-cbrt
28×unpow-prod-down cube-prod
13×add-cbrt-cube
9×associate-/r* add-exp-log
8×pow1
7×sum-cubes
6×associate-*r* add-log-exp
4×flip3-+ associate-/r/ flip-+ insert-posit16
3×prod-exp cbrt-unprod associate-/l* unswap-sqr
2×frac-times cbrt-undiv exp-prod div-exp pow-prod-down associate-*r/ *-commutative div-inv
1×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in flip3-- distribute-rgt-out-- diff-log associate-*l/ pow-prod-up flip--
Counts
4 → 147
Calls
4 calls:
Slowest
245.0ms
(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
40.0ms
(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
26.0ms
(* (exp a) (exp b))
13.0ms
(- (* (exp b) (exp b)) (* (exp a) (exp b)))

series356.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
187.0ms
(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
91.0ms
(/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))
55.0ms
(- (* (exp b) (exp b)) (* (exp a) (exp b)))
23.0ms
(* (exp a) (exp b))

simplify24.2s

Counts
149 → 159
Calls
149 calls:
Slowest
817.0ms
(* (* (* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))) (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3)))) (* (* (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))))
502.0ms
(/ (exp a) (+ (pow (pow (exp a) 3) 3) (pow (pow (exp b) 3) 3)))
455.0ms
(* (exp a) (- (* (* (exp a) (exp a)) (* (exp a) (exp a))) (* (- (* (exp b) (exp b)) (* (exp a) (exp b))) (- (* (exp b) (exp b)) (* (exp a) (exp b))))))
404.0ms
(/ (* (cbrt (exp a)) (cbrt (exp a))) (* (cbrt (+ (pow (exp a) 3) (pow (exp b) 3))) (cbrt (+ (pow (exp a) 3) (pow (exp b) 3)))))
383.0ms
(/ (sqrt (exp a)) (+ (pow (exp a) 3) (pow (exp b) 3)))

prune2.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (* (exp b) (exp b)) (* (exp a) (exp b)))
1.0b
(* (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
0.7b
(/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))
0.4b
(* (exp a) (exp b))

rewrite698.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
26×*-un-lft-identity
25×times-frac
24×add-cube-cbrt
21×associate-*l*
13×add-cbrt-cube
9×add-exp-log
8×pow1
7×cube-unmult pow3 sum-cubes
6×associate-*r* add-log-exp
4×associate-/r* flip3-+ associate-/r/ flip-+ insert-posit16
3×prod-exp cbrt-unprod associate-/l* unswap-sqr
2×frac-times cbrt-undiv exp-prod div-exp pow-prod-down associate-*r/ *-commutative div-inv
1×distribute-rgt-in clear-num sub-neg frac-2neg distribute-lft-in flip3-- distribute-rgt-out-- diff-log associate-*l/ pow-prod-up flip--
Counts
4 → 112
Calls
4 calls:
Slowest
480.0ms
(* (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
172.0ms
(/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))
27.0ms
(- (* (exp b) (exp b)) (* (exp a) (exp b)))
17.0ms
(* (exp a) (exp b))

series374.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
207.0ms
(* (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
91.0ms
(/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))
55.0ms
(- (* (exp b) (exp b)) (* (exp a) (exp b)))
21.0ms
(* (exp a) (exp b))

simplify14.6s

Counts
99 → 124
Calls
99 calls:
Slowest
868.0ms
(* (/ (* (* (exp a) (exp a)) (exp a)) (* (* (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a)))) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))) (* (* (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))))
763.0ms
(* (* (* (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a)))) (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))) (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))) (* (* (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))))
624.0ms
(* (sqrt (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a))))) (sqrt (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b))))))
505.0ms
(* (exp a) (- (* (* (exp a) (exp a)) (* (exp a) (exp a))) (* (- (* (exp b) (exp b)) (* (exp a) (exp b))) (- (* (exp b) (exp b)) (* (exp a) (exp b))))))
401.0ms
(* (/ (exp a) (+ (* (exp b) (* (exp b) (exp b))) (* (* (exp a) (exp a)) (exp a)))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))

prune1.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

regimes172.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch1.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
3.5s3541×body10240exit
671.0ms8000×body80valid