Details

Time bar (total: 47.9s)

sample906.0ms

Algorithm
intervals
Results
546.0ms114×body1280valid
160.0ms72×body2560valid
91.0ms41×body10240exit
35.0ms39×body640valid
30.0ms8×body320valid
15.0ms297×pre80true
4.0ms19×body80valid
2.0ms4×body160valid

simplify407.0ms

Calls
1 calls:
Slowest
407.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.2b

localize62.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (exp (* (+ a b) eps)) 1)
2.8b
(- (exp (* a eps)) 1)
2.4b
(- (exp (* b eps)) 1)
1.0b
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×flip3-- flip--
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×sub-neg difference-of-sqr-1
4×frac-times associate-*r* associate-*l* insert-posit16 add-log-exp
2×distribute-rgt-in distribute-lft-in associate-*l/ associate-*r/
1×pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
31.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
7.0ms
(- (exp (* (+ a b) eps)) 1)
5.0ms
(- (exp (* a eps)) 1)
5.0ms
(- (exp (* b eps)) 1)

series242.0ms

Calls
4 calls:
Slowest
78.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
64.0ms
(- (exp (* (+ a b) eps)) 1)
51.0ms
(- (exp (* b eps)) 1)
50.0ms
(- (exp (* a eps)) 1)

simplify4.5s

Calls
41 calls:
Slowest
332.0ms
(* (- (pow (exp (* a eps)) 3) (pow 1 3)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
323.0ms
(* (- (pow (exp (* a eps)) 3) (pow 1 3)) (- (exp (* b eps)) 1))
276.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (pow (exp (* b eps)) 3) (pow 1 3)))
267.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
253.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 42.0b

localize41.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (exp (* (+ a b) eps)) 1)
2.9b
(/ (* 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)))))))
2.8b
(- (exp (* a eps)) 1)
2.5b
(+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
9×add-cbrt-cube add-exp-log
8×associate-/r/
6×add-sqr-sqrt flip3-- flip-- add-log-exp
4×frac-times pow1 *-un-lft-identity flip3-+ associate-*r/ add-cube-cbrt flip-+ insert-posit16
2×cbrt-undiv sub-neg difference-of-sqr-1 div-exp associate-*l/ associate-/l/
1×+-commutative clear-num associate-/r* sum-log frac-2neg times-frac prod-exp cbrt-unprod div-inv associate-/l*
Calls
4 calls:
Slowest
35.0ms
(/ (* 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)))))))
14.0ms
(- (exp (* (+ a b) eps)) 1)
9.0ms
(- (exp (* a eps)) 1)
9.0ms
(+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b))))

series2.1s

Calls
4 calls:
Slowest
1.8s
(/ (* 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)))))))
178.0ms
(+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* (* (* eps b) (* eps b)) (* eps b))))
62.0ms
(- (exp (* a eps)) 1)
54.0ms
(- (exp (* (+ a b) eps)) 1)

simplify7.0s

Calls
32 calls:
Slowest
726.0ms
(* (+ (* (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))))))))
624.0ms
(* (+ (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))))))))
463.0ms
(+ (* 1/2 (* (pow eps 2) (pow b 2))) (* 1/6 (* (pow eps 3) (pow b 3))))
411.0ms
(+ (* (* 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)))))))
397.0ms
(+ (* 1/2 (* (pow eps 2) (pow b 2))) (* 1/6 (* (pow eps 3) (pow b 3))))

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

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
4.0ms
(+ (/ 1 a) (/ 1 b))

series13.0ms

Calls
1 calls:
Slowest
13.0ms
(+ (/ 1 a) (/ 1 b))

simplify155.0ms

Calls
10 calls:
Slowest
22.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 b) (/ 1 a))
18.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(+ (/ 1 a) (/ 1 b))

prune157.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
0.5b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.5b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.5b
(cbrt (+ (/ 1 a) (/ 1 b)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
35×cbrt-prod
33×cbrt-div
31×*-un-lft-identity
20×div-inv distribute-lft-out
11×add-sqr-sqrt flip3-+ frac-add add-cube-cbrt flip-+
10×associate-*r* associate-*l*
9×frac-times pow1
7×pow1/3
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×pow-prod-down pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
28.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
9.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
5.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
5.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series431.0ms

Calls
4 calls:
Slowest
121.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
112.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
107.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
92.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

simplify8.9s

Calls
94 calls:
Slowest
455.0ms
(- (+ (pow (/ 1 b) 1/3) (* 1/3 (* (/ 1 a) (pow (pow b 2) 1/3)))) (* 1/9 (* (/ 1 (pow a 2)) (pow (pow b 5) 1/3))))
454.0ms
(- (+ (pow (/ 1 b) 1/3) (* 1/3 (* (/ 1 a) (pow (pow b 2) 1/3)))) (* 1/9 (* (/ 1 (pow a 2)) (pow (pow b 5) 1/3))))
433.0ms
(- (+ (pow (/ 1 b) 1/3) (* 1/3 (* (/ 1 a) (pow (pow b 2) 1/3)))) (* 1/9 (* (/ 1 (pow a 2)) (pow (pow b 5) 1/3))))
405.0ms
(- (+ (* 2/3 (* (/ 1 a) (pow b 1/3))) (pow (/ 1 b) 2/3)) (* 1/9 (* (/ 1 (pow a 2)) (pow (pow b 4) 1/3))))
388.0ms
(* (cbrt (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes159.0ms

Accuracy

0% (3.2b remaining)

Error of 3.4b against oracle of 0.2b and baseline of 3.4b

bsearch1.0ms

end0.0ms

sample19.0s

Algorithm
intervals
Results
6.5s2649×body2560valid
5.3s3350×body1280valid
4.5s1879×body10240exit
976.0ms1067×body640valid
727.0ms349×body320valid
537.0ms9879×pre80true
79.0ms462×body80valid
42.0ms123×body160valid