Details

Time bar (total: 53.1s)

sample560.0ms

Algorithm
intervals
Results
185.0ms75×body2560valid
185.0ms114×body1280valid
110.0ms55×body10240exit
26.0ms31×body640valid
15.0ms311×pre80true
10.0ms16×body320valid
3.0ms15×body80valid
2.0ms5×body160valid

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
288.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.3b

localize53.0ms

Local error

Found 4 expressions with local error:

5.1b
(- (exp (* (+ a b) eps)) 1)
3.4b
(- (exp (* a eps)) 1)
2.8b
(- (exp (* b eps)) 1)
0.7b
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×*-un-lft-identity
10×add-log-exp difference-of-squares
9×flip3-- flip--
7×associate-*r* associate-*l*
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
5×sub-neg difference-of-sqr-1 distribute-lft-out--
4×frac-times insert-posit16
3×diff-log
2×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
90.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
21.0ms
(- (exp (* b eps)) 1)
15.0ms
(- (exp (* a eps)) 1)
12.0ms
(- (exp (* (+ a b) eps)) 1)

series230.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(- (exp (* (+ a b) eps)) 1)
63.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
47.0ms
(- (exp (* a eps)) 1)
39.0ms
(- (exp (* b eps)) 1)

simplify12.4s

Counts
66 → 102
Calls
66 calls:
Slowest
613.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
464.0ms
(+ (* (exp (* b eps)) (exp (* b eps))) (+ (* 1 1) (* (exp (* b eps)) 1)))
435.0ms
(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
427.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
411.0ms
(* (- (exp (* eps b)) 1) (- (exp (* a eps)) 1))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 45.0b

localize81.0ms

Local error

Found 4 expressions with local error:

5.1b
(- (exp (* (+ a b) eps)) 1)
3.1b
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
3.0b
(+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))
2.8b
(- (exp (* b eps)) 1)

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
13×add-log-exp
12×add-sqr-sqrt
10×*-un-lft-identity
8×associate-/r/
6×flip3-- flip--
4×frac-times pow1 cbrt-undiv flip3-+ div-exp prod-exp associate-*r/ add-cube-cbrt cbrt-unprod flip-+ insert-posit16 difference-of-squares
3×sum-log
2×sub-neg diff-log difference-of-sqr-1 associate-*l/ distribute-lft-out-- associate-/l/
1×+-commutative associate-+l+ clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
Slowest
1.2s
(+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))
866.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
13.0ms
(- (exp (* (+ a b) eps)) 1)
11.0ms
(- (exp (* b eps)) 1)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))) (- (exp (* b eps)) 1)))
123.0ms
(+ (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))
54.0ms
(- (exp (* b eps)) 1)
48.0ms
(- (exp (* (+ a b) eps)) 1)

simplify11.4s

Counts
50 → 92
Calls
50 calls:
Slowest
759.0ms
(* (+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps)))))) (+ (exp (* b eps)) 1))
623.0ms
(+ (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps))) (- (* (* 1/2 (* (* a eps) (* a eps))) (* 1/2 (* (* a eps) (* a eps)))) (* (+ (* eps (* (* 1/6 a) (* (* a eps) (* a eps)))) (* a eps)) (* 1/2 (* (* a eps) (* a eps))))))
545.0ms
(/ (exp (exp (* (+ a b) eps))) (exp 1))
442.0ms
(* eps (* (* 1/6 a) (* (* a eps) (* a eps))))
432.0ms
(+ (* (exp (* b eps)) (exp (* b eps))) (+ (* 1 1) (* (exp (* b eps)) 1)))

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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-+ insert-posit16
Counts
1 → 20
Calls
1 calls:
Slowest
21.0ms
(+ (/ 1 a) (/ 1 b))

series22.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
22.0ms
(+ (/ 1 a) (/ 1 b))

simplify205.0ms

Counts
16 → 23
Calls
16 calls:
Slowest
32.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
21.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 b) (/ 1 a))
17.0ms
(+ (/ 1 a) (/ 1 b))

prune163.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 1 expressions with local error:

13.7b
(/ (+ b a) (* a b))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-cbrt-cube add-exp-log
4×times-frac associate-/l*
3×add-sqr-sqrt add-cube-cbrt
2×cbrt-undiv div-exp distribute-lft-out associate-/l/
1×pow1 clear-num associate-/r* frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ insert-posit16 div-inv add-log-exp
Counts
1 → 26
Calls
1 calls:
Slowest
20.0ms
(/ (+ b a) (* a b))

series46.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
46.0ms
(/ (+ b a) (* a b))

simplify721.0ms

Counts
19 → 29
Calls
19 calls:
Slowest
274.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
193.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
53.0ms
(- (log (+ b a)) (+ (log a) (log b)))
39.0ms
(- (log (+ b a)) (log (* a b)))
33.0ms
(- (* b b) (* a a))

prune250.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes186.0ms

Accuracy

0% (3.0b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 3.1b

bsearch2.0ms

end0.0ms

sample19.8s

Algorithm
intervals
Results
6.8s3489×body1280valid
5.8s2535×body2560valid
4.7s1931×body10240exit
1.2s1074×body640valid
529.0ms9933×pre80true
362.0ms360×body320valid
147.0ms416×body80valid
52.0ms128×body160valid