Details

Time bar (total: 3.1m)

sample1.1s

Algorithm
intervals
Results
386.0ms141×body10240exit
233.0ms115×body1280valid
164.0ms78×body640valid
104.0ms50×body1280nan
42.0ms39×body640nan
34.0ms43×body320valid
28.0ms28×body320nan
8.0ms13×body160valid
7.0ms14×body160nan
4.0ms11×body80valid
3.0ms12×body80nan

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 3 (506.0ms)

IterNodesCost
05594
113394
244792
3247489
done500289

prune67.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.7b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
1.0b
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
1.0b
(sqrt (* PI 2.0))
1.2b
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))

rewrite1.2m

Algorithm
rewrite-expression-head
Rules
624×frac-add
176×flip3-+ flip-+
157×*-un-lft-identity
117×distribute-lft-out
80×frac-times associate-*r/
31×associate-*r*
27×add-exp-log
20×associate-*l* add-cbrt-cube
19×add-sqr-sqrt
14×prod-exp
12×add-cube-cbrt
9×pow1
8×times-frac div-exp
7×unpow-prod-down
6×associate-+l- cbrt-unprod
4×cbrt-undiv associate-/r* add-log-exp unswap-sqr
3×pow-to-exp exp-sum associate-*l/ pow-exp
2×sqrt-pow1 exp-diff pow-prod-down sqrt-prod associate-/r/ *-commutative div-inv pow-sub sqr-pow
1×unpow-prod-up distribute-rgt-in frac-2neg distribute-lft-in pow1/2 clear-num associate-/l/ associate-/l* distribute-lft-out--
Counts
4 → 286
Calls
4 calls:
854.0ms
(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
942.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
4.0ms
(sqrt (* PI 2.0))
1.2m
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))

series2.0s

Counts
4 → 10
Calls
4 calls:
651.0ms
(/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
453.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms
(sqrt (* PI 2.0))
933.0ms
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))

simplify817.0ms

Counts
296 → 296
Iterations

Useful iterations: done (715.0ms)

IterNodesCost
0107363253
done500058696

prune6.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (sqrt 2.0) (exp 6.5))
1.0b
(* (log 6.5) (sqrt 2.0))
1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite527.0ms

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt
104×unpow-prod-down
84×times-frac
68×*-un-lft-identity
62×associate-*l*
56×add-cube-cbrt
53×add-exp-log
40×sqrt-prod
38×unswap-sqr
26×pow-exp
25×prod-exp
20×sqr-pow
18×associate-*r*
13×div-exp
12×add-cbrt-cube
8×pow-to-exp
7×pow1
6×rec-exp 1-exp associate-/l*
4×add-log-exp
3×associate-/r* *-commutative cbrt-unprod div-inv
1×cbrt-undiv frac-2neg pow-prod-down clear-num log-pow
Counts
4 → 210
Calls
4 calls:
12.0ms
(/ (sqrt 2.0) (exp 6.5))
11.0ms
(* (log 6.5) (sqrt 2.0))
52.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
429.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(/ (sqrt 2.0) (exp 6.5))
0.0ms
(* (log 6.5) (sqrt 2.0))
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify1.6s

Counts
214 → 214
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02763478
15743293
216213125
done50003073

prune3.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize133.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(/ (sqrt 2.0) (exp 6.5))
1.0b
(* (log 6.5) (sqrt 2.0))
1.0b
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
52×unpow-prod-down
51×times-frac
46×*-un-lft-identity
40×add-cube-cbrt
33×associate-*l*
31×sqrt-prod
30×add-exp-log
20×unswap-sqr
13×pow-exp prod-exp
12×associate-*r*
10×add-cbrt-cube sqr-pow
8×pow1
7×div-exp
6×associate-/l*
4×pow-to-exp add-log-exp
3×rec-exp 1-exp associate-/r*
2×*-commutative cbrt-unprod div-inv
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num log-pow
Counts
4 → 149
Calls
4 calls:
2.0ms
(sqrt PI)
18.0ms
(/ (sqrt 2.0) (exp 6.5))
22.0ms
(* (log 6.5) (sqrt 2.0))
104.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(sqrt PI)
0.0ms
(/ (sqrt 2.0) (exp 6.5))
0.0ms
(* (log 6.5) (sqrt 2.0))
0.0ms
(* (pow (/ 1 (pow 6.5 1.0)) 0.5) (sqrt PI))

simplify1.7s

Counts
153 → 153
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02822394
15842252
216292083
done50001983

prune2.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (* PI 2.0))
1.0b
(sqrt (* PI 2.0))
1.0b
(sqrt (* PI 2.0))
1.2b
(* (/ (* (* (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))

rewrite1.0m

Algorithm
rewrite-expression-head
Rules
624×frac-add
176×flip3-+ flip-+
143×*-un-lft-identity
112×distribute-lft-out
80×frac-times associate-*r/
27×associate-*r*
15×pow1 add-exp-log
14×add-cbrt-cube
9×add-sqr-sqrt associate-*l*
7×add-cube-cbrt prod-exp cbrt-unprod
6×sqrt-pow1
4×times-frac pow-prod-down add-log-exp
3×cbrt-undiv pow1/2 div-exp sqrt-prod
2×associate-+l-
1×distribute-rgt-in distribute-lft-in exp-diff exp-sum associate-*l/ associate-/r/ *-commutative div-inv unswap-sqr
Counts
4 → 250
Calls
4 calls:
3.0ms
(sqrt (* PI 2.0))
3.0ms
(sqrt (* PI 2.0))
3.0ms
(sqrt (* PI 2.0))
1.0m
(* (/ (* (* (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))

series670.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(sqrt (* PI 2.0))
0.0ms
(sqrt (* PI 2.0))
0.0ms
(sqrt (* PI 2.0))
670.0ms
(* (/ (* (* (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (cbrt (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))

simplify1.6s

Counts
256 → 256
Iterations

Useful iterations: done (1.5s)

IterNodesCost
098070707
1487166167
done500057023

prune4.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

0% (1.1b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 1.1b

bsearch0.0ms

simplify16.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
067152
199152
done99152

end0.0ms

sample24.7s

Algorithm
intervals
Results
8.3s3791×body10240exit
5.4s3379×body1280valid
3.9s2491×body640valid
3.0s1532×body1280nan
1.3s1246×body320valid
1.2s1263×body640nan
679.0ms628×body160valid
381.0ms659×body320nan
144.0ms329×body160nan
75.0ms357×body80valid
54.0ms290×body80nan