Details

Time bar (total: 3.4m)

sample1.5s

Algorithm
intervals
Results
761.0ms121×body10240exit
190.0ms99×body1280valid
115.0ms83×body640valid
110.0ms38×body1280nan
87.0ms40×body320valid
44.0ms38×body640nan
19.0ms24×body320nan
16.0ms25×body160valid
6.0ms11×body160nan
4.0ms11×body80valid
2.0ms6×body80nan

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (476.0ms)

IterNodesCost
05594
113394
244792
3285789
done500189

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize182.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
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))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
27×distribute-lft-out
22×times-frac
15×add-exp-log
14×add-sqr-sqrt
11×associate-*l* add-cbrt-cube
9×add-cube-cbrt
7×pow1 unpow-prod-down distribute-lft-out--
6×prod-exp add-log-exp
4×associate-+l- div-exp associate-*r* associate-/r*
3×unswap-sqr
2×cbrt-undiv pow-to-exp sqrt-pow1 exp-sum associate-*l/ pow-exp sqrt-prod cbrt-unprod pow-sub sqr-pow
1×unpow-prod-up +-commutative frac-2neg flip3-+ pow1/2 exp-diff pow-prod-down frac-add clear-num sum-log associate-/r/ *-commutative flip-+ div-inv associate-/l/ associate-/l*
Counts
4 → 91
Calls
4 calls:
309.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
999.0ms
(/ (* (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)))
1.0s
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
8.0ms
(sqrt (* PI 2.0))

series1.1s

Counts
4 → 10
Calls
4 calls:
108.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
583.0ms
(/ (* (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)))
436.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms
(sqrt (* PI 2.0))

simplify1.9s

Counts
101 → 101
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02812677
17852589
236052304
done50002293

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize100.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ (sqrt (* PI 2.0)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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))))))
0.9b
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ (sqrt (* PI 2.0)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
1.0b
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b
(sqrt (* PI 2.0))

rewrite1.4m

Algorithm
rewrite-expression-head
Rules
1689×frac-add
557×flip3-+ flip-+
442×frac-times
348×*-un-lft-identity
222×associate-*r/
198×distribute-lft-out
155×times-frac
126×add-sqr-sqrt
115×associate-*l/
84×sqrt-prod
83×associate-*l*
66×associate-*r*
62×add-exp-log
58×add-cube-cbrt
48×unpow-prod-down
34×add-cbrt-cube
25×prod-exp
21×unswap-sqr
20×div-exp
15×exp-sum
14×pow1
13×cbrt-unprod distribute-lft-out-- sqr-pow
8×cbrt-undiv
7×unpow-prod-up
6×add-log-exp
5×pow-prod-down
4×pow-to-exp associate-+l- pow-exp
2×sqrt-pow1 exp-diff sqrt-div associate-/r/ *-commutative div-inv
1×+-commutative distribute-rgt-in distribute-lft-in pow1/2 sum-log
Counts
4 → 696
Calls
4 calls:
1.3m
(* (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ (sqrt (* PI 2.0)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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))))))
4.4s
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ (sqrt (* PI 2.0)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
301.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
4.0ms
(sqrt (* PI 2.0))

series2.3s

Counts
4 → 10
Calls
4 calls:
985.0ms
(* (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ (sqrt (* PI 2.0)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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))))))
677.0ms
(* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ (sqrt (* PI 2.0)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
588.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
0.0ms
(sqrt (* PI 2.0))

simplify1.3s

Counts
706 → 706
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01767191667
done5002190106

prune17.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize208.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b
(* (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ 1 (sqrt (exp (+ (- z 1.0) 7.0))))) (/ (sqrt (* PI 2.0)) (sqrt (exp 0.5))))
1.0b
(/ (sqrt (* PI 2.0)) (sqrt (exp 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite8.7s

Algorithm
rewrite-expression-head
Rules
147×add-exp-log
92×*-un-lft-identity
66×times-frac prod-exp
58×div-exp
47×add-cbrt-cube
41×sqrt-prod
36×add-sqr-sqrt add-cube-cbrt
28×associate-*r*
22×distribute-lft-out
18×cbrt-unprod
14×cbrt-undiv
12×pow1
8×pow-to-exp rec-exp 1-exp pow-exp
6×frac-times associate-*l/ associate-/r* distribute-lft-out-- add-log-exp
4×pow-prod-down associate-/l*
3×associate-*r/
2×sqrt-pow1 un-div-inv div-inv
1×+-commutative sqrt-undiv frac-2neg flip3-+ pow1/2 associate-*l* frac-add clear-num sum-log *-commutative flip-+
Counts
4 → 172
Calls
4 calls:
284.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
8.3s
(* (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ 1 (sqrt (exp (+ (- z 1.0) 7.0))))) (/ (sqrt (* PI 2.0)) (sqrt (exp 0.5))))
24.0ms
(/ (sqrt (* PI 2.0)) (sqrt (exp 0.5)))
7.0ms
(sqrt (* PI 2.0))

series975.0ms

Counts
4 → 8
Calls
4 calls:
97.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
877.0ms
(* (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))) (/ 1 (sqrt (exp (+ (- z 1.0) 7.0))))) (/ (sqrt (* PI 2.0)) (sqrt (exp 0.5))))
0.0ms
(/ (sqrt (* PI 2.0)) (sqrt (exp 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify636.0ms

Counts
180 → 180
Iterations

Useful iterations: done (622.0ms)

IterNodesCost
03586541
111126093
done50015160

prune2.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize179.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0s

Algorithm
rewrite-expression-head
Rules
845×frac-add
279×flip3-+ flip-+
221×associate-/l/
120×associate-+l-
114×associate-*l/
112×pow-sub
111×frac-times associate-*r/
72×*-un-lft-identity
46×add-exp-log
27×add-cbrt-cube distribute-lft-out
22×prod-exp
19×times-frac
12×add-sqr-sqrt
11×associate-*l*
10×div-exp cbrt-unprod
7×pow1 add-cube-cbrt unpow-prod-down distribute-lft-out--
6×cbrt-undiv add-log-exp
4×exp-diff sqrt-div associate-*r*
3×pow-to-exp pow-exp associate-/r/ unswap-sqr
2×sqrt-pow1 sqrt-prod sqr-pow
1×unpow-prod-up +-commutative frac-2neg pow1/2 pow-prod-down clear-num associate-/r* sum-log *-commutative div-inv associate-/l*
Counts
4 → 317
Calls
4 calls:
26.7s
(/ (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (* (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
315.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
969.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
4.0ms
(sqrt (* PI 2.0))

series1.8s

Counts
4 → 10
Calls
4 calls:
844.0ms
(/ (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (+ (+ (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (* (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (sqrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))
91.0ms
(+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
873.0ms
(* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))
0.0ms
(sqrt (* PI 2.0))

simplify1.9s

Counts
327 → 327
Iterations

Useful iterations: done (1.8s)

IterNodesCost
084134204
1351929053
done500227786

prune9.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes344.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
062104
185104
done85104

end0.0ms

sample33.7s

Algorithm
intervals
Results
12.6s3813×body10240exit
7.5s3418×body1280valid
4.1s2467×body640valid
3.2s1453×body1280nan
1.7s1242×body640nan
1.7s1245×body320valid
937.0ms586×body320nan
907.0ms627×body160valid
194.0ms308×body160nan
117.0ms336×body80nan
83.0ms316×body80valid