Details

Time bar (total: 30.6s)

sample480.0ms

Algorithm
intervals
Results
156.0ms85×body2560valid
115.0ms105×body1280valid
99.0ms54×body10240exit
49.0ms310×pre80true
29.0ms38×body640valid
6.0ms10×body320valid
2.0ms6×body160valid
2.0ms12×body80valid

simplify970.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
52001
4694
3215
298
143
017

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 58.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
3.1b
(- (exp (* a eps)) 1)
3.9b
(- (exp (* b eps)) 1)
5.2b
(- (exp (* (+ a b) eps)) 1)

rewrite138.0ms

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:
88.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
16.0ms
(- (exp (* a eps)) 1)
15.0ms
(- (exp (* b eps)) 1)
18.0ms
(- (exp (* (+ a b) eps)) 1)

series198.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1))
44.0ms
(- (exp (* a eps)) 1)
39.0ms
(- (exp (* b eps)) 1)
62.0ms
(- (exp (* (+ a b) eps)) 1)

simplify1.0s

Counts
102 → 102
Iterations
IterNodes
done2001
32001
21367
1395
0154

prune524.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 46.8b

localize61.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
5.2b
(- (exp (* (+ a b) eps)) 1)
12.6b
(* (* eps eps) (* a a))
15.0b
(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

rewrite369.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
82×add-cbrt-cube add-exp-log
56×pow-prod-down
54×prod-exp cbrt-unprod
8×add-sqr-sqrt associate-/r/
7×*-un-lft-identity
6×add-log-exp
5×flip3-- flip--
4×frac-times cbrt-undiv pow-plus div-exp associate-*r/ pow-prod-up add-cube-cbrt insert-posit16
3×flip3-+ flip-+
2×pow2 associate-*r* associate-*l* associate-*l/ pow-sqr *-commutative difference-of-squares associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg times-frac diff-log difference-of-sqr-1 div-inv associate-/l* distribute-lft-out-- unswap-sqr
Counts
4 → 126
Calls
4 calls:
203.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
14.0ms
(- (exp (* (+ a b) eps)) 1)
22.0ms
(* (* eps eps) (* a a))
127.0ms
(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

series1.2s

Counts
4 → 12
Calls
4 calls:
987.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (+ (* (* 1/6 (* eps (* eps eps))) (* (* a a) a)) (+ (* eps a) (* 1/2 (* (* eps eps) (* a a))))) (- (exp (* b eps)) 1)))
61.0ms
(- (exp (* (+ a b) eps)) 1)
43.0ms
(* (* eps eps) (* a a))
83.0ms
(* (* 1/6 (* eps (* eps eps))) (* (* a a) a))

simplify1.2s

Counts
138 → 138
Iterations
IterNodes
done2003
22003
1795
0254

prune688.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite16.0ms

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:
15.0ms
(+ (/ 1 a) (/ 1 b))

series15.0ms

Counts
1 → 3
Calls
1 calls:
15.0ms
(+ (/ 1 a) (/ 1 b))

simplify1.2s

Counts
23 → 23
Iterations
IterNodes
done2012
52012
41333
3593
2278
1105
041

prune117.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
0.6b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b
(cbrt (+ (/ 1 a) (/ 1 b)))
0.6b
(cbrt (+ (/ 1 a) (/ 1 b)))

rewrite94.0ms

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
Counts
4 → 163
Calls
4 calls:
62.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
15.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
6.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
6.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
131.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
87.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))
92.0ms
(cbrt (+ (/ 1 a) (/ 1 b)))

simplify1.1s

Counts
175 → 175
Iterations
IterNodes
done2003
32003
21136
1426
0180

prune677.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes254.0ms

Accuracy

0% (3.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done9
19
06

end0.0ms

sample19.6s

Algorithm
intervals
Results
5.8s3487×body1280valid
5.8s2545×body2560valid
5.6s1929×body10240exit
959.0ms1063×body640valid
673.0ms9931×pre80true
269.0ms362×body320valid
75.0ms411×body80valid
48.0ms134×body160valid