Details

Time bar (total: 1.1m)

sample497.0ms

Algorithm
intervals
Results
166.0ms114×body1280valid
144.0ms72×body2560valid
85.0ms41×body10240exit
64.0ms39×body640valid
13.0ms297×pre80true
3.0ms8×body320valid
3.0ms19×body80valid
1.0ms4×body160valid

simplify370.0ms

Calls
1 calls:
Slowest
370.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.2b

localize47.0ms

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))

rewrite129.0ms

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
Calls
4 calls:
Slowest
88.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
17.0ms
(- (exp (* (+ a b) eps)) 1)
12.0ms
(- (exp (* b eps)) 1)
11.0ms
(- (exp (* a eps)) 1)

series235.0ms

Calls
4 calls:
Slowest
85.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
55.0ms
(- (exp (* (+ a b) eps)) 1)
51.0ms
(- (exp (* b eps)) 1)
44.0ms
(- (exp (* a eps)) 1)

simplify11.8s

Calls
66 calls:
Slowest
606.0ms
(* (- (* (exp (* a eps)) (exp (* a eps))) (* 1 1)) (- (* (exp (* b eps)) (exp (* b eps))) (* 1 1)))
562.0ms
(* (sqrt (- (exp (* a eps)) 1)) (sqrt (- (exp (* b eps)) 1)))
433.0ms
(* (+ (* (exp (* a eps)) (exp (* a eps))) (+ (* 1 1) (* (exp (* a eps)) 1))) (+ (exp (* b eps)) 1))
394.0ms
(* (+ (exp (* a eps)) 1) (+ (exp (* b eps)) 1))
383.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 42.0b

localize67.0ms

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)))))))))
2.9b
(* eps (* b (* (* eps b) (* eps b))))
2.8b
(- (exp (* a eps)) 1)

rewrite411.0ms

Algorithm
rewrite-expression-head
Rules
41×add-cbrt-cube add-exp-log
29×pow1
23×prod-exp cbrt-unprod
19×pow-prod-down
13×add-sqr-sqrt
11×*-un-lft-identity
8×associate-/r/ add-log-exp
6×flip3-- flip--
5×add-cube-cbrt
4×frac-times cbrt-undiv div-exp associate-*r/ insert-posit16 difference-of-squares
3×flip3-+ associate-*l* flip-+
2×sub-neg diff-log difference-of-sqr-1 associate-*l/ distribute-lft-out-- associate-/l/
1×clear-num associate-/r* frac-2neg times-frac associate-*r* *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
201.0ms
(/ (* 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)))))))))
185.0ms
(* eps (* b (* (* eps b) (* eps b))))
13.0ms
(- (exp (* (+ a b) eps)) 1)
11.0ms
(- (exp (* a eps)) 1)

series2.0s

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)))))))))
106.0ms
(* eps (* b (* (* eps b) (* eps b))))
60.0ms
(- (exp (* (+ a b) eps)) 1)
40.0ms
(- (exp (* a eps)) 1)

simplify14.2s

Calls
68 calls:
Slowest
983.0ms
(* (+ (* (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))))))))))
789.0ms
(* (+ (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))))))))))
499.0ms
(+ (* (* 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)))))))))
447.0ms
(* (* (* eps eps) eps) (* (* (* b b) b) (* (* (* (* eps b) (* eps b)) (* (* eps b) (* eps b))) (* (* eps b) (* eps b)))))
417.0ms
(+ (* eps b) (+ (* 1/2 (* (* eps b) (* eps b))) (* 1/6 (* eps (* b (* (* eps b) (* eps b)))))))

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite18.0ms

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

series12.0ms

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

simplify188.0ms

Calls
16 calls:
Slowest
23.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
17.0ms
(+ (/ 1 a) (/ 1 b))
16.0ms
(+ (/ 1 a) (/ 1 b))
16.0ms
(+ (/ 1 b) (/ 1 a))
15.0ms
(+ (/ 1 a) (/ 1 b))

prune242.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

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)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
139×*-un-lft-identity
114×cbrt-prod
81×distribute-lft-out
60×div-inv
42×times-frac
37×add-sqr-sqrt
33×cbrt-div swap-sqr
29×add-cube-cbrt
13×associate-*r* associate-*l*
11×pow1 flip3-+ frac-add flip-+
9×frac-times pow1/3
6×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
3×associate-*l/ associate-*r/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
63.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
15.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
13.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
13.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series536.0ms

Calls
4 calls:
Slowest
170.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
141.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
119.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
106.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

simplify10.2s

Calls
187 calls:
Slowest
677.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))
336.0ms
(* (cbrt (+ (* 1 b) (* a 1))) (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))))
327.0ms
(* (cbrt (+ (pow (/ 1 a) 3) (pow (/ 1 b) 3))) (cbrt (+ (* 1 b) (* a 1))))
323.0ms
(* (cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b)))) (cbrt (+ (/ 1 a) (/ 1 b))))
307.0ms
(cbrt (- (* (/ 1 a) (/ 1 a)) (* (/ 1 b) (/ 1 b))))

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

0% (3.2b remaining)

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

bsearch2.0ms

end0.0ms

sample19.2s

Algorithm
intervals
Results
7.1s2649×body2560valid
5.0s3350×body1280valid
4.6s1879×body10240exit
1.2s1067×body640valid
632.0ms9879×pre80true
196.0ms349×body320valid
121.0ms462×body80valid
48.0ms123×body160valid