Details

Time bar (total: 52.1s)

sample594.0ms

Algorithm
intervals
Results
246.0ms121×body1280valid
170.0ms74×body2560valid
89.0ms43×body10240exit
32.0ms33×body640valid
16.0ms299×pre80true
8.0ms8×body320valid
3.0ms14×body80valid
2.0ms6×body160valid

simplify406.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
405.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.7b

localize55.0ms

Local error

Found 4 expressions with local error:

5.3b
(- (exp (* (+ a b) eps)) 1)
3.6b
(- (exp (* b eps)) 1)
3.2b
(- (exp (* a eps)) 1)
1.2b
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

rewrite196.0ms

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
121.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
28.0ms
(- (exp (* (+ a b) eps)) 1)
23.0ms
(- (exp (* a eps)) 1)
23.0ms
(- (exp (* b eps)) 1)

series184.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(- (exp (* (+ a b) eps)) 1)
55.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
35.0ms
(- (exp (* a eps)) 1)
32.0ms
(- (exp (* b eps)) 1)

simplify12.4s

Counts
66 → 102
Calls
66 calls:
Slowest
679.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
468.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
442.0ms
(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
432.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
373.0ms
(* (- (exp (* eps b)) 1) (- (exp (* a eps)) 1))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.1b

localize53.0ms

Local error

Found 4 expressions with local error:

5.3b
(- (exp (* (+ a b) eps)) 1)
4.1b
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
3.2b
(- (exp (* a eps)) 1)
2.0b
(+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))

rewrite295.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
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
2×sub-neg diff-log difference-of-sqr-1 associate-*l/ distribute-lft-out-- associate-/l/
1×+-commutative clear-num associate-/r* sum-log frac-2neg times-frac div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
166.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
86.0ms
(+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))
31.0ms
(- (exp (* (+ a b) eps)) 1)
11.0ms
(- (exp (* a eps)) 1)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))
143.0ms
(+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))
50.0ms
(- (exp (* (+ a b) eps)) 1)
40.0ms
(- (exp (* a eps)) 1)

simplify10.7s

Counts
48 → 90
Calls
48 calls:
Slowest
828.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))))))
573.0ms
(* (+ (exp (* a eps)) 1) (+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))))))
527.0ms
(+ (* 1/2 (* (pow eps 2) (pow b 2))) (* 1/6 (* (pow eps 3) (pow b 3))))
475.0ms
(+ (* 1/2 (* (pow eps 2) (pow b 2))) (* 1/6 (* (pow eps 3) (pow b 3))))
449.0ms
(+ (* (* eps b) (* eps b)) (- (* (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b))))))) (* (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))))

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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
10.0ms
(+ (/ 1 a) (/ 1 b))

series13.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
12.0ms
(+ (/ 1 a) (/ 1 b))

simplify199.0ms

Counts
16 → 23
Calls
16 calls:
Slowest
23.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
20.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
19.0ms
(+ (/ (sqrt 1) a) (/ (sqrt 1) b))
18.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 a) (/ 1 b))

prune230.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

16.6b
(/ (+ b a) (* a b))

rewrite33.0ms

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
32.0ms
(/ (+ b a) (* a b))

series47.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
47.0ms
(/ (+ b a) (* a b))

simplify786.0ms

Counts
19 → 29
Calls
19 calls:
Slowest
268.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
241.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
71.0ms
(- (log (+ b a)) (+ (log a) (log b)))
46.0ms
(+ (pow b 3) (pow a 3))
36.0ms
(- (log (+ b a)) (log (* a b)))

prune243.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes177.0ms

Accuracy

0% (3.4b remaining)

Error of 3.5b against oracle of 0.2b and baseline of 3.5b

bsearch1.0ms

end0.0ms

sample20.1s

Algorithm
intervals
Results
7.0s2591×body2560valid
6.0s3420×body1280valid
4.4s1881×body10240exit
1.4s1040×body640valid
573.0ms9882×pre80true
242.0ms344×body320valid
88.0ms479×body80valid
47.0ms127×body160valid