Details

Time bar (total: 45.8s)

sample383.0ms

Algorithm
intervals
Results
109.0ms50×body10240exit
107.0ms67×body2560valid
100.0ms117×body1280valid
18.0ms37×body640valid
8.0ms306×pre80true
4.0ms13×body320valid
2.0ms18×body80valid
1.0ms4×body160valid

simplify1.5s

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.3b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b
(- (exp (* b eps)) 1.0)
2.7b
(- (exp (* a eps)) 1.0)
4.1b
(- (exp (* (+ a b) eps)) 1.0)

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
10×add-log-exp
9×flip3-- flip--
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×sub-neg associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
4×frac-times
3×diff-log
2×distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 76
Calls
4 calls:
99.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
12.0ms
(- (exp (* b eps)) 1.0)
12.0ms
(- (exp (* a eps)) 1.0)
15.0ms
(- (exp (* (+ a b) eps)) 1.0)

series230.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
52.0ms
(- (exp (* b eps)) 1.0)
40.0ms
(- (exp (* a eps)) 1.0)
69.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify750.0ms

Counts
88 → 88

prune447.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.9b

localize55.0ms

Local error

Found 4 expressions with local error:

2.9b
(* (+ (* (/ 1 6) (* (pow a 3) (pow eps 3))) (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
4.1b
(- (exp (* (+ a b) eps)) 1.0)
10.8b
(* (pow a 2) (pow eps 2))
12.8b
(* (pow a 3) (pow eps 3))

rewrite511.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
33×unswap-sqr
30×add-exp-log
28×unpow-prod-down
25×associate-*r*
23×associate-*l*
20×*-un-lft-identity sqr-pow
19×prod-exp
16×add-cube-cbrt
14×cube-prod
12×pow-to-exp pow-exp
10×associate-*l/ add-cbrt-cube unpow2
8×frac-times
6×pow1 flip3-- flip3-+ frac-add flip-- flip-+ add-log-exp
3×sub-neg pow-prod-down *-commutative cbrt-unprod
2×distribute-rgt-in cube-mult distribute-lft-in unpow3 associate-*r/ distribute-lft-out-- difference-of-squares
1×diff-log
Counts
4 → 162
Calls
4 calls:
404.0ms
(* (+ (* (/ 1 6) (* (pow a 3) (pow eps 3))) (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
23.0ms
(- (exp (* (+ a b) eps)) 1.0)
40.0ms
(* (pow a 2) (pow eps 2))
33.0ms
(* (pow a 3) (pow eps 3))

series364.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (+ (* (/ 1 6) (* (pow a 3) (pow eps 3))) (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0))
79.0ms
(- (exp (* (+ a b) eps)) 1.0)
39.0ms
(* (pow a 2) (pow eps 2))
75.0ms
(* (pow a 3) (pow eps 3))

simplify570.0ms

Counts
174 → 174

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 48.7b

localize49.0ms

Local error

Found 4 expressions with local error:

2.5b
(+ (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps)) (/ (pow (* a eps) 3) 6))
2.9b
(* (- (exp (* b eps)) 1.0) (+ (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps)) (/ (pow (* a eps) 3) 6)))
4.1b
(- (exp (* (+ a b) eps)) 1.0)
10.8b
(* (pow a 2) (pow eps 2))

rewrite708.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
18×add-exp-log *-un-lft-identity
17×unswap-sqr
14×unpow-prod-down
13×associate-*l*
12×associate-*r*
11×add-log-exp
10×add-cube-cbrt prod-exp unpow2 sqr-pow
8×frac-times flip3-+ frac-add add-cbrt-cube flip-+
6×pow1 pow-to-exp flip3-- pow-exp flip--
4×associate-*r/
3×sum-log
2×pow-prod-down associate-*l/ *-commutative cbrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in sub-neg associate-+l+ distribute-lft-in diff-log
Counts
4 → 118
Calls
4 calls:
183.0ms
(+ (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps)) (/ (pow (* a eps) 3) 6))
487.0ms
(* (- (exp (* b eps)) 1.0) (+ (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps)) (/ (pow (* a eps) 3) 6)))
15.0ms
(- (exp (* (+ a b) eps)) 1.0)
18.0ms
(* (pow a 2) (pow eps 2))

series610.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(+ (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps)) (/ (pow (* a eps) 3) 6))
353.0ms
(* (- (exp (* b eps)) 1.0) (+ (+ (* (/ 1 2) (* (pow a 2) (pow eps 2))) (* a eps)) (/ (pow (* a eps) 3) 6)))
73.0ms
(- (exp (* (+ a b) eps)) 1.0)
50.0ms
(* (pow a 2) (pow eps 2))

simplify2.4s

Counts
130 → 130

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 48.3b

localize75.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16))
10.8b
(* (pow a 2) (pow eps 2))
11.3b
(* (pow a 2) (* (pow eps 2) (exp (* eps b))))
37.3b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (pow (- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16)) 1))

rewrite15.8s

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
36×add-sqr-sqrt
33×prod-exp add-log-exp
29×unpow-prod-down *-un-lft-identity
16×associate-*l* add-cbrt-cube unswap-sqr
15×pow-to-exp pow-exp
14×add-cube-cbrt
13×diff-log sqr-pow
11×unpow2
10×times-frac associate-/r* frac-sub
9×associate-*r* sum-log distribute-lft-out--
6×div-exp
5×cbrt-unprod
4×pow1 flip3-+ associate--l+ flip-+
3×flip3-- flip-- difference-of-squares
2×cbrt-undiv sub-neg associate-*r/ *-commutative associate-/l/
1×associate--l- frac-2neg pow-prod-down clear-num div-inv associate-/l*
Counts
4 → 154
Calls
4 calls:
5.9s
(- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16))
36.0ms
(* (pow a 2) (pow eps 2))
53.0ms
(* (pow a 2) (* (pow eps 2) (exp (* eps b))))
9.8s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (pow (- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16)) 1))

series1.8s

Counts
4 → 12
Calls
4 calls:
288.0ms
(- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16))
56.0ms
(* (pow a 2) (pow eps 2))
59.0ms
(* (pow a 2) (* (pow eps 2) (exp (* eps b))))
1.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (pow (- (- (+ (+ (/ (* 1 (* (pow (* a eps) 3) (exp (* eps b)))) 6) (* (/ 1 2) (* (pow a 2) (* (pow eps 2) (exp (* eps b)))))) (* a (* eps (exp (* eps b))))) (+ (* (/ 1.0 2.0) (* (pow a 2) (pow eps 2))) (* 1.0 (* a eps)))) (/ (* 6004799503160661.0 (pow (* a eps) 3)) 3.602879701896397e+16)) 1))

simplify825.0ms

Counts
166 → 166

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes148.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify23.0ms

end0.0ms

sample14.5s

Algorithm
intervals
Results
4.4s3530×body1280valid
4.1s2528×body2560valid
3.9s1971×body10240exit
765.0ms9977×pre80true
606.0ms1025×body640valid
116.0ms365×body320valid
44.0ms449×body80valid
23.0ms109×body160valid