Details

Time bar (total: 32.4s)

sample379.0ms

Algorithm
intervals
Results
128.0ms92×body2560valid
110.0ms53×body10240exit
88.0ms108×body1280valid
13.0ms30×body640valid
8.0ms309×pre80true
2.0ms17×body80valid
2.0ms6×body320valid
1.0ms3×body160valid

simplify2.3s

Counts
1 → 1
Iterations
IterNodes
done5001
53569
4699
3245
2101
140
017

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* b eps))
2.7b
(- (exp (* a eps)) 1.0)
3.6b
(- (exp (* b eps)) 1.0)
5.6b
(- (exp (* (+ a b) eps)) 1.0)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
12×add-log-exp
10×add-sqr-sqrt *-un-lft-identity
4×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
3×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
1×exp-prod exp-to-pow rem-exp-log
Counts
4 → 52
Calls
4 calls:
4.0ms
(exp (* b eps))
20.0ms
(- (exp (* a eps)) 1.0)
14.0ms
(- (exp (* b eps)) 1.0)
16.0ms
(- (exp (* (+ a b) eps)) 1.0)

series174.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(exp (* b eps))
47.0ms
(- (exp (* a eps)) 1.0)
44.0ms
(- (exp (* b eps)) 1.0)
66.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify2.4s

Counts
64 → 64
Iterations
IterNodes
done5000
34344
2852
1248
0114

prune453.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 49.8b

localize144.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (- (exp (* a eps)) 1.0) (+ (* (* 1/2 (* b eps)) (* b eps)) (* b (+ eps (* 1/6 (* eps (* (* b eps) (* b eps))))))))
2.7b
(- (exp (* a eps)) 1.0)
3.9b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* (* 1/2 (* b eps)) (* b eps)) (* b (+ eps (* 1/6 (* eps (* (* b eps) (* b eps)))))))))
5.6b
(- (exp (* (+ a b) eps)) 1.0)

rewrite400.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
12×*-un-lft-identity
9×flip3-- flip--
8×frac-times associate-/r/ add-log-exp
6×pow1 flip3-+ associate-*r/ add-cube-cbrt flip-+
5×associate-*l* prod-exp cbrt-unprod
4×cbrt-undiv div-exp associate-*l/
3×associate-*r* distribute-lft-out-- difference-of-squares
2×sub-neg diff-log associate-/l/
1×distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in times-frac pow-prod-down *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 89
Calls
4 calls:
249.0ms
(* (- (exp (* a eps)) 1.0) (+ (* (* 1/2 (* b eps)) (* b eps)) (* b (+ eps (* 1/6 (* eps (* (* b eps) (* b eps))))))))
17.0ms
(- (exp (* a eps)) 1.0)
111.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* (* 1/2 (* b eps)) (* b eps)) (* b (+ eps (* 1/6 (* eps (* (* b eps) (* b eps)))))))))
21.0ms
(- (exp (* (+ a b) eps)) 1.0)

series2.9s

Counts
4 → 12
Calls
4 calls:
345.0ms
(* (- (exp (* a eps)) 1.0) (+ (* (* 1/2 (* b eps)) (* b eps)) (* b (+ eps (* 1/6 (* eps (* (* b eps) (* b eps))))))))
66.0ms
(- (exp (* a eps)) 1.0)
2.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* (* 1/2 (* b eps)) (* b eps)) (* b (+ eps (* 1/6 (* eps (* (* b eps) (* b eps)))))))))
79.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify1.9s

Counts
101 → 101
Iterations
IterNodes
done5001
1818
0245

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (/ 1 a) (/ 1 b))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
7×distribute-lft-out
6×times-frac
4×div-inv
3×add-sqr-sqrt add-cube-cbrt add-log-exp
1×pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+
Counts
1 → 19
Calls
1 calls:
20.0ms
(+ (/ 1 a) (/ 1 b))

series13.0ms

Counts
1 → 3
Calls
1 calls:
13.0ms
(+ (/ 1 a) (/ 1 b))

simplify1.4s

Counts
22 → 22
Iterations
IterNodes
done5000
31500
2381
1102
040

prune118.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
3.5b
(+ (* (/ 1 b) (* (/ 1 b) (/ 1 b))) (/ (* (/ 1 a) (/ 1 a)) a))
4.8b
(- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))
44.4b
(/ (+ (* (/ 1 b) (* (/ 1 b) (/ 1 b))) (/ (* (/ 1 a) (/ 1 a)) a)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
210×frac-add
177×associate-*r/
169×un-div-inv
144×associate-*l/ frac-sub
132×frac-times
98×associate-/r/
54×sub-div
13×add-log-exp
12×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×associate-/l/
9×times-frac flip3-- flip--
6×add-cbrt-cube add-exp-log
4×pow1 flip3-+ flip-+
3×associate-/r* sum-log associate-/l*
2×+-commutative associate-+r+ sub-neg diff-log
1×cbrt-undiv clear-num associate-+r- frac-2neg distribute-rgt-out-- div-exp div-inv
Counts
4 → 302
Calls
4 calls:
73.0ms
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
77.0ms
(+ (* (/ 1 b) (* (/ 1 b) (/ 1 b))) (/ (* (/ 1 a) (/ 1 a)) a))
15.0ms
(- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))
300.0ms
(/ (+ (* (/ 1 b) (* (/ 1 b) (/ 1 b))) (/ (* (/ 1 a) (/ 1 a)) a)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))

series173.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b))))
50.0ms
(+ (* (/ 1 b) (* (/ 1 b) (/ 1 b))) (/ (* (/ 1 a) (/ 1 a)) a))
31.0ms
(- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))
70.0ms
(/ (+ (* (/ 1 b) (* (/ 1 b) (/ 1 b))) (/ (* (/ 1 a) (/ 1 a)) a)) (+ (* (/ 1 a) (/ 1 a)) (- (* (/ 1 b) (/ 1 b)) (* (/ 1 a) (/ 1 b)))))

simplify1.3s

Counts
314 → 314
Iterations
IterNodes
done5001
11423
0508

prune915.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes245.0ms

Accuracy

90.5% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 3.3b

bsearch4.0ms

simplify15.0ms

Iterations
IterNodes
done39
139
027

end0.0ms

sample15.3s

Algorithm
intervals
Results
4.9s2558×body2560valid
4.3s1964×body10240exit
3.9s3434×body1280valid
1.1s1098×body640valid
341.0ms9968×pre80true
210.0ms346×body320valid
47.0ms444×body80valid
27.0ms124×body160valid