Details

Time bar (total: 30.8s)

sample557.0ms

Algorithm
intervals
Results
204.0ms97×body2560valid
145.0ms89×body1280valid
117.0ms63×body10240exit
47.0ms43×body640valid
15.0ms319×pre80true
4.0ms8×body320valid
2.0ms16×body80valid
2.0ms3×body160valid

simplify509.0ms

Calls
1 calls:
Slowest
508.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.9b

localize40.0ms

Local error

Found 4 expressions with local error:

6.6b
(- (exp (* (+ a b) eps)) 1)
4.5b
(- (exp (* b eps)) 1)
2.7b
(- (exp (* a eps)) 1)
0.5b
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
10×flip3-- flip--
9×add-cbrt-cube add-exp-log
8×associate-/r/
7×add-sqr-sqrt
4×frac-times pow1 *-un-lft-identity associate-*r/ add-cube-cbrt insert-posit16 add-log-exp
3×sub-neg difference-of-sqr-1
2×cbrt-undiv div-exp associate-*l/ associate-/l/
1×clear-num associate-/r* frac-2neg times-frac prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
48.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
19.0ms
(- (exp (* a eps)) 1)
13.0ms
(- (exp (* (+ a b) eps)) 1)
10.0ms
(- (exp (* b eps)) 1)

series343.0ms

Calls
4 calls:
Slowest
200.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))
61.0ms
(- (exp (* (+ a b) eps)) 1)
44.0ms
(- (exp (* a eps)) 1)
38.0ms
(- (exp (* b eps)) 1)

simplify5.8s

Calls
32 calls:
Slowest
1.1s
(/ (* (* (* eps (- (exp (* (+ a b) eps)) 1)) (* eps (- (exp (* (+ a b) eps)) 1))) (* eps (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))))
916.0ms
(/ (* (* (* eps (- (exp (* (+ a b) eps)) 1)) (* eps (- (exp (* (+ a b) eps)) 1))) (* eps (- (exp (* (+ a b) eps)) 1))) (* (* (* (- (exp (* a eps)) 1) (- (exp (* a eps)) 1)) (- (exp (* a eps)) 1)) (* (* (- (exp (* b eps)) 1) (- (exp (* b eps)) 1)) (- (exp (* b eps)) 1))))
383.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
339.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
313.0ms
(- (log (* eps (- (exp (* (+ a b) eps)) 1))) (+ (log (- (exp (* a eps)) 1)) (log (- (exp (* b eps)) 1))))

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×div-inv distribute-lft-out
3×add-log-exp
1×add-sqr-sqrt pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log add-cube-cbrt flip-+ insert-posit16
Calls
1 calls:
Slowest
9.0ms
(+ (/ 1 a) (/ 1 b))

series7.0ms

Calls
1 calls:
Slowest
7.0ms
(+ (/ 1 a) (/ 1 b))

simplify114.0ms

Calls
10 calls:
Slowest
17.0ms
(+ (/ 1 b) (/ 1 a))
17.0ms
(+ (/ 1 b) (/ 1 a))
16.0ms
(+ (/ 1 a) (/ 1 b))
15.0ms
(+ (/ 1 a) (/ 1 b))
12.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))

prune194.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity times-frac add-cbrt-cube add-exp-log add-cube-cbrt associate-/l*
2×associate-/l/
1×pow1 cbrt-undiv clear-num associate-/r* frac-2neg flip3-+ div-exp flip-+ insert-posit16 div-inv add-log-exp
Calls
1 calls:
Slowest
7.0ms
(/ (+ b a) (* a b))

series32.0ms

Calls
1 calls:
Slowest
32.0ms
(/ (+ b a) (* a b))

simplify382.0ms

Calls
15 calls:
Slowest
193.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
40.0ms
(- (log (+ b a)) (log (* a b)))
24.0ms
(- (* b b) (* a a))
22.0ms
(/ (* (cbrt (+ b a)) (cbrt (+ b a))) a)
19.0ms
(+ (/ 1 a) (/ 1 b))

prune190.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

5.8b
(* (/ (sqrt (+ b a)) a) (/ (sqrt (+ b a)) b))
0.1b
(/ (sqrt (+ b a)) b)
0.1b
(/ (sqrt (+ b a)) a)
0.0b
(sqrt (+ b a))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt associate-/l*
11×*-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×pow1 add-cbrt-cube sqrt-div add-exp-log
4×associate-*r* associate-*l* insert-posit16 div-inv add-log-exp associate-/l/
3×flip3-+ flip-+
2×clear-num frac-2neg
1×frac-times rem-sqrt-square pow1/2 pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
14.0ms
(* (/ (sqrt (+ b a)) a) (/ (sqrt (+ b a)) b))
7.0ms
(/ (sqrt (+ b a)) b)
7.0ms
(/ (sqrt (+ b a)) a)
1.0ms
(sqrt (+ b a))

series126.0ms

Calls
4 calls:
Slowest
36.0ms
(/ (sqrt (+ b a)) a)
33.0ms
(* (/ (sqrt (+ b a)) a) (/ (sqrt (+ b a)) b))
32.0ms
(/ (sqrt (+ b a)) b)
24.0ms
(sqrt (+ b a))

simplify959.0ms

Calls
45 calls:
Slowest
427.0ms
(* (* (* (/ (sqrt (+ b a)) a) (/ (sqrt (+ b a)) a)) (/ (sqrt (+ b a)) a)) (* (* (/ (sqrt (+ b a)) b) (/ (sqrt (+ b a)) b)) (/ (sqrt (+ b a)) b)))
119.0ms
(+ (log (/ (sqrt (+ b a)) a)) (log (/ (sqrt (+ b a)) b)))
77.0ms
(* (/ (sqrt (+ b a)) a) (/ (sqrt (+ b a)) b))
61.0ms
(sqrt (- (* b b) (* a a)))
42.0ms
(sqrt (- (* b b) (* a a)))

prune687.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes139.0ms

Accuracy

0% (3.3b remaining)

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

bsearch1.0ms

end0.0ms

sample19.3s

Algorithm
intervals
Results
6.7s2616×body2560valid
5.4s3370×body1280valid
4.6s1967×body10240exit
1.4s1086×body640valid
539.0ms9969×pre80true
232.0ms351×body320valid
85.0ms460×body80valid
43.0ms119×body160valid