Details

Time bar (total: 18.3s)

sample253.0ms

Algorithm
intervals
Results
101.0ms63×body1280valid
50.0ms63×body10240exit
33.0ms299×body80valid
25.0ms39×body640valid
7.0ms20×body320valid
3.0ms13×body160valid

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done5000
42266
3377
2122
146
019

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (- (* (- 1.0 eps) x)))
0.2b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.2b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
81×exp-neg frac-sub
80×frac-times
61×neg-sub0 exp-diff
40×associate-*l/ associate-*r/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×exp-prod associate-*r* add-exp-log
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac diff-log neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 168
Calls
4 calls:
15.0ms
(exp (- (* (- 1.0 eps) x)))
88.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
93.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
43.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(exp (- (* (- 1.0 eps) x)))
64.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
78.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
315.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify477.0ms

Counts
180 → 180
Iterations
IterNodes
done5001
11223
0380

prune963.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (pow x 3) 0.6666666666666667)
6.6b
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
7×add-exp-log add-log-exp
6×*-un-lft-identity add-cube-cbrt
4×unpow-prod-down add-cbrt-cube cube-prod unswap-sqr
3×associate-*r* prod-exp
2×pow1 associate-+r+ sum-log sqr-pow
1×cube-mult pow-to-exp +-commutative associate-+r- sub-neg flip3-+ diff-log unpow3 pow-exp *-commutative cbrt-unprod flip-+
Counts
2 → 46
Calls
2 calls:
10.0ms
(* (pow x 3) 0.6666666666666667)
13.0ms
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series126.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(* (pow x 3) 0.6666666666666667)
77.0ms
(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify766.0ms

Counts
52 → 52
Iterations
IterNodes
done5002
21044
1215
083

prune229.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
6.6b
(+ (* (pow (* (cbrt x) (cbrt x)) 3) (* 0.6666666666666667 x)) (- 2.0 (* 1.0 (* x x))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×pow1
9×add-log-exp
8×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube unswap-sqr
2×associate-+r+ sum-log pow-prod-down pow-sqr pow-prod-up
1×pow2 +-commutative associate-+r- sub-neg flip3-+ pow-plus diff-log prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 77
Calls
4 calls:
9.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
28.0ms
(+ (* (pow (* (cbrt x) (cbrt x)) 3) (* 0.6666666666666667 x)) (- 2.0 (* 1.0 (* x x))))

series967.0ms

Counts
4 → 12
Calls
4 calls:
301.0ms
(* (cbrt x) (cbrt x))
322.0ms
(cbrt x)
256.0ms
(cbrt x)
88.0ms
(+ (* (pow (* (cbrt x) (cbrt x)) 3) (* 0.6666666666666667 x)) (- 2.0 (* 1.0 (* x x))))

simplify920.0ms

Counts
89 → 89
Iterations
IterNodes
done5001
21379
1266
0101

prune468.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
6.6b
(+ (* (pow (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) 3) (* 0.6666666666666667 x)) (- 2.0 (* 1.0 (* x x))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-log-exp
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log
3×pow1/3
2×associate-+r+ sum-log
1×+-commutative associate-+r- sub-neg flip3-+ diff-log flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
50.0ms
(+ (* (pow (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) 3) (* 0.6666666666666667 x)) (- 2.0 (* 1.0 (* x x))))

series944.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(cbrt x)
296.0ms
(cbrt x)
263.0ms
(cbrt x)
101.0ms
(+ (* (pow (* (cbrt x) (* (* (cbrt (cbrt x)) (cbrt (cbrt x))) (cbrt (cbrt x)))) 3) (* 0.6666666666666667 x)) (- 2.0 (* 1.0 (* x x))))

simplify415.0ms

Counts
60 → 60
Iterations
IterNodes
done5001
2833
1187
069

prune383.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes118.0ms

Accuracy

96% (0.7b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 17.2b

bsearch219.0ms

Steps
ItersRangePoint
10
1.5375988180684124e-09
886.592532349027
162.56045792773165

simplify7.0ms

Iterations
IterNodes
done58
258
152
036

end0.0ms

sample8.9s

Algorithm
intervals
Results
2.8s1832×body10240exit
2.3s1703×body1280valid
1.6s9991×body80valid
838.0ms1290×body640valid
441.0ms314×body160valid
243.0ms599×body320valid