Details

Time bar (total: 18.4s)

sample239.0ms

Algorithm
intervals
Results
91.0ms78×body10240exit
47.0ms57×body1280valid
36.0ms286×body80valid
21.0ms43×body640valid
5.0ms16×body320valid
3.0ms14×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
01929
14629
212229
337727
4226727
done500027

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize76.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
2.4b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 173
Calls
4 calls:
87.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
103.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
36.0ms
(* (- 1.0 eps) x)
82.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
69.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
36.0ms
(* (- 1.0 eps) x)
291.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify711.0ms

Counts
185 → 185
Iterations

Useful iterations: done (699.0ms)

IterNodesCost
03978268
112667516
done50007195

prune953.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
7.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
14.0ms
(* 0.6666666666666667 (pow x 3))
104.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series121.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(* 0.6666666666666667 (pow x 3))
54.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify673.0ms

Counts
51 → 51
Iterations

Useful iterations: done (671.0ms)

IterNodesCost
084590
1222548
2908500
done5000462

prune233.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))) (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))))
12.8b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
12.8b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
12.8b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
52.0ms
(* (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))) (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))))
3.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
3.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
3.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))) (cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0)))))
177.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
202.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
194.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

simplify941.0ms

Counts
99 → 99
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
01763286
14363055
217132839
done50002475

prune518.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize64.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
12.8b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
12.8b
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log cbrt-div pow1/3 add-cbrt-cube add-log-exp
2×flip3-+ flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt 2.0)
1.0ms
(cbrt 2.0)
3.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
3.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

series386.0ms

Counts
4 → 8
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
188.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))
198.0ms
(cbrt (+ 2.0 (* (* x x) (- (* x 0.6666666666666667) 1.0))))

simplify681.0ms

Counts
56 → 56
Iterations

Useful iterations: done (677.0ms)

IterNodesCost
01091116
12651078
29991002
done5001900

prune438.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes158.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.1b

bsearch212.0ms

Steps
ItersRangePoint
9
0.13444838907100976
28949269.581200972
174.50277220888506

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03258
14658
25258
done5258

end0.0ms

sample8.8s

Algorithm
intervals
Results
2.6s9933×body80valid
2.6s1919×body10240exit
1.9s1806×body1280valid
792.0ms1234×body640valid
211.0ms643×body320valid
65.0ms318×body160valid