Details

Time bar (total: 4.5m)

sample1.7s

Algorithm
intervals
Results
784.0ms132×body10240exit
328.0ms96×body1280valid
145.0ms88×body640valid
125.0ms48×body1280nan
74.0ms46×body640nan
55.0ms48×body320valid
21.0ms16×body320nan
14.0ms17×body160valid
9.0ms13×body160nan
5.0ms11×body80valid
4.0ms11×body80nan

simplify972.0ms

Counts
1 → 1
Iterations
IterNodes
32125
2412
1139
055

prune61.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize149.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
1.0b
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
1.0b
(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
1.0b
(sqrt (* PI 2))

rewrite15.7s

Algorithm
rewrite-expression-head
Rules
444×frac-add
157×*-un-lft-identity
152×flip3-+ flip-+
117×distribute-lft-out
68×frac-times associate-*r/
32×associate-*r*
27×add-exp-log
20×add-cbrt-cube
19×add-sqr-sqrt associate-*l*
14×prod-exp
12×add-cube-cbrt
9×pow1
8×times-frac div-exp
6×unpow-prod-down cbrt-unprod
4×expm1-log1p-u cbrt-undiv associate-/r* associate-+l- log1p-expm1-u add-log-exp unswap-sqr
3×pow-to-exp exp-sum associate-*l/ pow-exp
2×sqrt-pow1 exp-diff pow-prod-down associate-/r/ *-commutative sqrt-prod div-inv pow-sub sqr-pow
1×distribute-rgt-in unpow-prod-up clear-num frac-2neg distribute-lft-in pow1/2 associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 270
Calls
4 calls:
124.0ms
(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
15.4s
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
160.0ms
(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
6.0ms
(sqrt (* PI 2))

series1.9s

Counts
4 → 10
Calls
4 calls:
595.0ms
(/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5)))
872.0ms
(* (/ (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (- z -6) 0.5))) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
416.0ms
(* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2)))
0.0ms
(sqrt (* PI 2))

simplify7.2s

Counts
280 → 280
Iterations
IterNodes
14665
0935

prune12.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize139.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
1.0b
(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
1.0b
(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
1.0b
(sqrt (* PI 2))

rewrite27.0s

Algorithm
rewrite-expression-head
Rules
1332×frac-add
504×*-un-lft-identity
456×flip3-+ flip-+
341×frac-times associate-*r/
293×times-frac
231×exp-sum
224×add-sqr-sqrt
219×add-cube-cbrt
189×prod-diff
173×distribute-lft-out
161×associate-*l*
145×unpow-prod-down
39×add-exp-log
32×add-cbrt-cube
29×unpow-prod-up associate-*r* distribute-lft-out-- sqr-pow
22×prod-exp
21×sub-neg
17×div-exp
14×pow1 associate-/r*
12×cbrt-unprod
10×associate-/l*
7×cbrt-undiv
5×distribute-rgt-in distribute-lft-in pow-prod-down
4×expm1-log1p-u pow-to-exp associate-*l/ pow-exp sqrt-prod log1p-expm1-u add-log-exp
3×div-inv
2×sqrt-pow1 exp-diff associate-/r/ *-commutative unswap-sqr
1×clear-num frac-2neg pow1/2 associate-+l- pow-sub associate-/l/
Counts
4 → 850
Calls
4 calls:
15.1s
(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
11.7s
(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
130.0ms
(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
7.0ms
(sqrt (* PI 2))

series2.3s

Counts
4 → 10
Calls
4 calls:
485.0ms
(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
1.5s
(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
289.0ms
(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- z -6)))
0.0ms
(sqrt (* PI 2))

simplify11.3s

Counts
860 → 860
Iterations
IterNodes
16925
01644

prune39.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize172.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
0.9b
(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
1.0b
(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
1.0b
(sqrt (* PI 2))

rewrite27.1s

Algorithm
rewrite-expression-head
Rules
1332×frac-add
456×flip3-+ flip-+
341×frac-times associate-*r/
224×*-un-lft-identity
129×distribute-lft-out
73×times-frac
54×add-sqr-sqrt
52×associate-*l*
49×add-cube-cbrt
39×add-exp-log
35×unpow-prod-down
32×add-cbrt-cube
29×associate-*r*
22×prod-exp
17×div-exp
14×pow1
12×cbrt-unprod
10×associate-/l*
7×cbrt-undiv unpow-prod-up distribute-lft-out-- sqr-pow
5×distribute-rgt-in distribute-lft-in pow-prod-down
4×expm1-log1p-u pow-to-exp associate-*l/ pow-exp associate-/r/ sqrt-prod log1p-expm1-u add-log-exp
3×associate-/r* div-inv
2×neg-sub0 exp-neg sqrt-pow1 exp-diff *-commutative unswap-sqr
1×clear-num frac-2neg pow1/2 associate-+l- pow-sub associate-/l/
Counts
4 → 621
Calls
4 calls:
15.2s
(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
11.8s
(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
99.0ms
(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
4.0ms
(sqrt (* PI 2))

series1.7s

Counts
4 → 10
Calls
4 calls:
469.0ms
(* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3)))))
960.0ms
(* (/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6))) (* (/ (sqrt (* PI 2)) (exp 0.5)) (+ (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))) (+ (/ -0.13857109526572012 (+ -1 (- z -6))) (/ 12.507343278686905 (+ z 4)))) (+ (+ (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z)))) (/ -1259.1392167224028 (- z -1))) (/ -176.6150291621406 (+ z 3))))))
283.0ms
(/ (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (exp (- -6)))
0.0ms
(sqrt (* PI 2))

simplify12.2s

Counts
631 → 631
Iterations
IterNodes
16544
01458

prune36.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize234.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
1.0b
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
1.0b
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
1.0b
(/ (sqrt 2) (exp 6.5))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
178×add-sqr-sqrt
156×unpow-prod-down
117×times-frac
88×*-un-lft-identity
87×associate-*r*
74×add-exp-log
70×add-cube-cbrt
54×unswap-sqr
48×sqrt-prod
39×pow-exp
36×prod-exp
30×sqr-pow
19×div-exp
18×associate-*l*
12×pow-to-exp add-cbrt-cube
9×rec-exp 1-exp
6×associate-/l*
4×expm1-log1p-u pow1 log1p-expm1-u div-inv add-log-exp
3×associate-/r* *-commutative cbrt-unprod
1×cbrt-undiv clear-num frac-2neg
Counts
4 → 269
Calls
4 calls:
40.0ms
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
37.0ms
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
37.0ms
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
14.0ms
(/ (sqrt 2) (exp 6.5))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
0.0ms
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
0.0ms
(* (sqrt PI) (pow (/ 1 (pow 6.5 1.0)) 0.5))
0.0ms
(/ (sqrt 2) (exp 6.5))

simplify6.2s

Counts
273 → 273
Iterations
IterNodes
34877
21511
1568
0268

prune12.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

0% (0.8b remaining)

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

bsearch0.0ms

simplify18.0ms

Iterations
IterNodes
278
178
058

end0.0ms

sample50.1s

Algorithm
intervals
Results
15.9s3872×body10240exit
11.1s3363×body1280valid
7.7s2468×body640valid
5.6s1579×body1280nan
4.1s1290×body640nan
2.3s1275×body320valid
1.5s644×body320nan
678.0ms621×body160valid
400.0ms338×body160nan
173.0ms387×body80valid
143.0ms323×body80nan