Details

Time bar (total: 1.2m)

sample430.0ms

Algorithm
intervals
Results
128.0ms126×body10240exit
89.0ms98×body1280valid
60.0ms91×body640valid
38.0ms58×body1280nan
24.0ms46×body640nan
15.0ms34×body320valid
8.0ms21×body320nan
6.0ms19×body160valid
5.0ms19×body160nan
3.0ms21×body80valid
0.0ms4×body80nan

simplify957.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (231.0ms)

IterNodesCost
05594
113394
244492
3249389
done500189

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
0.9b
(+ (+ (/ 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))))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
1059×*-un-lft-identity
494×distribute-lft-out
346×times-frac
115×distribute-lft-out--
16×add-log-exp
15×add-exp-log add-sqr-sqrt frac-add
13×fma-def
11×associate-*r* add-cbrt-cube
10×add-cube-cbrt
8×sum-log
7×pow1 unpow-prod-down flip3-+ flip-+
6×prod-exp
4×expm1-log1p-u associate-+l- div-exp associate-*l* associate-/r* log1p-expm1-u
3×unswap-sqr
2×cbrt-undiv pow-to-exp sqrt-pow1 associate-*r/ exp-sum pow-exp sqrt-prod cbrt-unprod pow-sub sqr-pow
1×unpow-prod-up +-commutative associate-+l+ associate-+r+ frac-2neg pow1/2 exp-diff pow-prod-down clear-num associate-/r/ *-commutative div-inv associate-/l/ associate-/l*
Counts
4 → 200
Calls
4 calls:
314.0ms
(/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
983.0ms
(+ (+ (/ 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))))
320.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series813.0ms

Counts
4 → 10
Calls
4 calls:
401.0ms
(/ (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (+ (+ (- z 1.0) 7.0) 0.5)))
141.0ms
(+ (+ (/ 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))))
269.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify1.3s

Counts
210 → 210
Iterations

Useful iterations: 2 (442.0ms)

IterNodesCost
03647039
111456745
249026452
done50006452

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 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))))))
0.9b
(+ (+ (/ 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))))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite20.2s

Algorithm
rewrite-expression-head
Rules
4257×frac-add
1547×flip3-+ flip-+
1259×*-un-lft-identity
1250×frac-times
942×associate-*r/
660×distribute-lft-out
472×associate-+l- pow-sub
471×exp-neg
342×times-frac
314×neg-sub0 exp-diff
163×associate-*l/
157×un-div-inv
115×distribute-lft-out--
49×associate-*r*
21×add-exp-log
16×add-log-exp
15×prod-exp add-cbrt-cube
14×add-sqr-sqrt
13×fma-def
12×pow1
9×add-cube-cbrt
8×sum-log
7×unpow-prod-down cbrt-unprod
5×associate-*l*
4×expm1-log1p-u pow-prod-down log1p-expm1-u
3×unswap-sqr
2×pow-to-exp sqrt-pow1 pow-exp sqrt-prod *-commutative sqr-pow
1×unpow-prod-up +-commutative distribute-rgt-in associate-+l+ associate-+r+ distribute-lft-in pow1/2
Counts
4 → 1330
Calls
4 calls:
18.6s
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 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))))))
986.0ms
(+ (+ (/ 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))))
322.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series1.0s

Counts
4 → 10
Calls
4 calls:
617.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (+ (/ 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))))))
151.0ms
(+ (+ (/ 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))))
280.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify1.9s

Counts
1340 → 1340
Iterations

Useful iterations: 0 (797.0ms)

IterNodesCost
02689456363
done5000456363

prune22.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize119.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
1.0b
(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))

rewrite506.0ms

Algorithm
rewrite-expression-head
Rules
376×*-un-lft-identity
200×times-frac
132×add-sqr-sqrt
103×add-cube-cbrt
101×distribute-lft-out
78×swap-sqr
53×associate-*r*
49×distribute-lft-out--
46×associate-*l*
33×add-exp-log
30×add-cbrt-cube
21×pow1
16×associate-/r/
11×prod-exp unswap-sqr
9×cbrt-unprod
8×cbrt-undiv flip3-+ div-exp flip-+ div-inv
7×unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ pow-prod-down *-commutative
2×pow2 frac-times sqrt-pow1 pow-plus associate-*l/ sqrt-prod pow-sqr pow-prod-up sqr-pow
1×unpow-prod-up pow-to-exp associate-+l- pow1/2 pow-exp pow-sub
Counts
4 → 268
Calls
4 calls:
86.0ms
(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
85.0ms
(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
311.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))

series350.0ms

Counts
4 → 10
Calls
4 calls:
40.0ms
(* (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (/ -176.6150291621406 (+ (- z 1.0) 4.0)))
35.0ms
(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
275.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))

simplify537.0ms

Counts
278 → 278
Iterations

Useful iterations: done (523.0ms)

IterNodesCost
04716566
114685808
done50015709

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
1.0b
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
1.0b
(sqrt (* PI 2.0))
35.3b
(log (exp (* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))))

rewrite414.0ms

Algorithm
rewrite-expression-head
Rules
197×*-un-lft-identity
100×times-frac
73×add-sqr-sqrt
56×add-cube-cbrt
53×distribute-lft-out
39×swap-sqr
32×associate-*r*
25×associate-*l* distribute-lft-out--
21×add-exp-log
18×add-cbrt-cube
15×pow1
8×associate-/r/
7×unpow-prod-down prod-exp unswap-sqr
5×cbrt-unprod add-log-exp
4×cbrt-undiv expm1-log1p-u flip3-+ div-exp flip-+ log1p-expm1-u div-inv
3×log-prod log-pow
2×sqrt-pow1 associate-*r/ pow-prod-down sqrt-prod *-commutative sqr-pow
1×unpow-prod-up pow2 frac-times pow-to-exp associate-+l- exp-prod exp-to-pow pow-plus pow1/2 rem-log-exp associate-*l/ pow-exp pow-sqr pow-prod-up pow-sub
Counts
4 → 173
Calls
4 calls:
87.0ms
(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
315.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
2.0ms
(sqrt (* PI 2.0))
1.0ms
(log (exp (* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))))

series354.0ms

Counts
4 → 10
Calls
4 calls:
34.0ms
(* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))
283.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
0.0ms
(sqrt (* PI 2.0))
36.0ms
(log (exp (* (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)))))

simplify1.1s

Counts
183 → 183
Iterations

Useful iterations: 2 (497.0ms)

IterNodesCost
02944015
18103595
228333181
done50013181

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes225.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
091510
1129510
2134510
done134510

end0.0ms

sample11.8s

Algorithm
intervals
Results
4.1s3922×body10240exit
3.0s3390×body1280valid
1.6s2516×body640valid
1.0s1530×body1280nan
689.0ms1346×body640nan
539.0ms1237×body320valid
243.0ms652×body320nan
170.0ms606×body160valid
77.0ms314×body160nan
54.0ms344×body80valid
37.0ms309×body80nan