Details

Time bar (total: 8.4m)

sample2.2s

Algorithm
intervals
Results
1.9s143×body10240exit
61.0ms38×body1280nan
61.0ms259×body80valid
35.0ms38×body640nan
5.0ms12×body160nan
5.0ms7×body320nan
2.0ms9×body80nan

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (689.0ms)

IterNodesCost
060123
1148123
2609121
3384688
done500188

prune50.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize74.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (- 1.0 z) 1.0)
5.0b
(- (- 1.0 z) 1.0)
5.0b
(- (- 1.0 z) 1.0)
5.0b
(- (- 1.0 z) 1.0)

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity add-log-exp
12×add-sqr-sqrt diff-log distribute-lft-out--
8×sub-neg associate--l+
4×pow1 add-exp-log associate--l- add-cube-cbrt flip3-- add-cbrt-cube flip-- difference-of-squares
Counts
4 → 76
Calls
4 calls:
43.0ms
(- (- 1.0 z) 1.0)
56.0ms
(- (- 1.0 z) 1.0)
35.0ms
(- (- 1.0 z) 1.0)
45.0ms
(- (- 1.0 z) 1.0)

series60.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(- (- 1.0 z) 1.0)
12.0ms
(- (- 1.0 z) 1.0)
19.0ms
(- (- 1.0 z) 1.0)
17.0ms
(- (- 1.0 z) 1.0)

simplify2.2s

Counts
88 → 88
Iterations

Useful iterations: 4 (692.0ms)

IterNodesCost
038660
175628
2164588
3511464
41666424
done5000424

prune1.6s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize94.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.9m

Algorithm
rewrite-expression-head
Rules
634×frac-add
137×frac-times flip3-+ associate-*r/ flip-+
125×*-un-lft-identity
74×distribute-lft-out
73×add-log-exp
54×sum-log
51×associate-*l*
44×times-frac
37×add-exp-log
25×add-cbrt-cube
24×add-sqr-sqrt add-cube-cbrt unpow-prod-down
20×prod-exp
13×div-exp
12×pow1
11×exp-sum
10×cbrt-unprod
5×cbrt-undiv
4×unpow-prod-up distribute-rgt-in associate-+r- distribute-rgt-neg-in distribute-lft-in pow-prod-down sqr-pow
3×pow-to-exp exp-diff associate-*l/ pow-exp associate-/r/
2×+-commutative associate-+r+ sqrt-pow1
1×neg-sub0 associate-+l+ pow1/2 associate-*r* unsub-neg sqrt-prod *-commutative div-inv
Counts
4 → 321
Calls
4 calls:
369.0ms
(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
40.0s
(+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))
3.0ms
(sqrt (* PI 2.0))
4.2m
(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))))

series761.0ms

Counts
4 → 10
Calls
4 calls:
73.0ms
(+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))))
173.0ms
(+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))
0.0ms
(sqrt (* PI 2.0))
514.0ms
(* (/ (pow (+ 0.5 (+ 7.0 (- z))) (+ (- z) 0.5)) (exp (+ 0.5 (+ 7.0 (- z))))) (* (/ PI (sin (* PI z))) (+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z))))))))

simplify1.4s

Counts
331 → 331
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0110167583
1431557513
done500056490

prune4.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
1.0b
(+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z)))
1.0b
(+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z)))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (/ 12.507343278686905 (- 5.0 z)))) (/ -176.6150291621406 (- 4.0 z)))
1.0b
(sqrt (* PI 2.0))

rewrite41.6s

Algorithm
rewrite-expression-head
Rules
180×frac-add
152×*-un-lft-identity
105×add-log-exp
92×distribute-lft-out
82×sum-log
44×times-frac
41×flip3-+ flip-+
26×add-sqr-sqrt add-cube-cbrt
25×unpow-prod-down
12×exp-sum
11×associate-/l*
10×unpow-prod-up
7×pow1
6×add-exp-log add-cbrt-cube
5×sub-neg distribute-lft-out-- sqr-pow
4×associate-/r*
3×div-exp
2×+-commutative associate-+l+ sqrt-pow1
1×cbrt-undiv pow-to-exp associate-+l- frac-2neg pow1/2 exp-diff pow-prod-down pow-exp clear-num sqrt-prod associate-/r/ div-inv associate-/l/ pow-sub
Counts
4 → 192
Calls
4 calls:
186.0ms
(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
685.0ms
(+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z)))
40.7s
(+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z)))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (/ 12.507343278686905 (- 5.0 z)))) (/ -176.6150291621406 (- 4.0 z)))
3.0ms
(sqrt (* PI 2.0))

series437.0ms

Counts
4 → 10
Calls
4 calls:
159.0ms
(/ (pow (+ (- 7.0 z) 0.5) (- 0.5 z)) (exp (+ (- 7.0 z) 0.5)))
77.0ms
(+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z)))
201.0ms
(+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (+ (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z)))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (/ 12.507343278686905 (- 5.0 z)))) (/ -176.6150291621406 (- 4.0 z)))
0.0ms
(sqrt (* PI 2.0))

simplify778.0ms

Counts
202 → 202
Iterations

Useful iterations: done (751.0ms)

IterNodesCost
080219681
1250418229
done500018054

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize113.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
1.0b
(pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)
1.0b
(sqrt (* PI 2.0))
1.0b
(+ (* (+ (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z))) (* (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (- (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))) -1259.1392167224028) (* (+ (pow (/ -0.13857109526572012 (- 6.0 z)) 3) (pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)) (- 2.0 z)))

rewrite931.0ms

Algorithm
rewrite-expression-head
Rules
7434×frac-add
3624×associate-*l/
3368×frac-times
2501×cube-div
2399×flip3-+ flip-+
1248×associate-*r/
1200×frac-sub
1030×flip3-- flip--
48×*-un-lft-identity
38×add-sqr-sqrt
30×times-frac
26×add-cube-cbrt unpow-prod-down cube-prod
9×pow1
8×add-exp-log add-cbrt-cube
6×pow-unpow distribute-lft-out distribute-lft-out-- add-log-exp difference-of-squares
4×associate-+r+ associate-/r/
3×pow-exp rem-cube-cbrt
2×distribute-rgt-in cube-mult pow-to-exp sub-neg pow-pow distribute-lft-in sqrt-pow1 unpow3 div-inv sqr-pow
1×cbrt-undiv +-commutative pow1/2 div-exp pow-prod-down sum-log sqrt-prod
Counts
4 → 2199
Calls
4 calls:
13.0ms
(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
204.0ms
(pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)
3.0ms
(sqrt (* PI 2.0))
166.0ms
(+ (* (+ (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z))) (* (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (- (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))) -1259.1392167224028) (* (+ (pow (/ -0.13857109526572012 (- 6.0 z)) 3) (pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)) (- 2.0 z)))

series764.0ms

Counts
4 → 10
Calls
4 calls:
45.0ms
(pow (/ -0.13857109526572012 (- 6.0 z)) 3)
74.0ms
(pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)
0.0ms
(sqrt (* PI 2.0))
644.0ms
(+ (* (+ (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z))) (* (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (- (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (/ -0.13857109526572012 (- 6.0 z))))) -1259.1392167224028) (* (+ (pow (/ -0.13857109526572012 (- 6.0 z)) 3) (pow (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) 3)) (- 2.0 z)))

simplify4.0s

Counts
2209 → 2209
Iterations

Useful iterations: 0 (1.1s)

IterNodesCost
07906829190
done7906829190

prune1.6m

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes279.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify19.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0116698
1174698
done174698

end0.0ms

sample43.7s

Algorithm
intervals
Results
39.0s3915×body10240exit
1.5s1506×body1280nan
1.4s8086×body80valid
847.0ms1276×body640nan
312.0ms637×body320nan
95.0ms293×body160nan
51.0ms293×body80nan
1.0ms2×body160valid