Details

Time bar (total: 10.0m)

sample1.6s

Algorithm
intervals
Results
1.4s128×body10240exit
47.0ms259×body80valid
45.0ms44×body1280nan
29.0ms42×body640nan
13.0ms17×body320nan
4.0ms12×body160nan
2.0ms10×body80nan

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: done (1.3s)

IterNodesCost
060123
1148123
2592121
3358788
done500078

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (sqrt (* PI 2.0))) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))) (/ 771.3234287776531 (- 3.0 z))))))
1.0b
(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))))
1.0b
(sqrt (* PI 2.0))
2.5b
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

rewrite25.1s

Algorithm
rewrite-expression-head
Rules
624×frac-add
185×flip3-+ flip-+
144×*-un-lft-identity
112×distribute-lft-out
82×associate-*l/
81×pow-sub
80×frac-times associate-*r/
25×associate-*r*
18×add-log-exp
14×add-exp-log
9×pow1 sum-log add-cbrt-cube
7×prod-exp
5×add-sqr-sqrt add-cube-cbrt
3×cbrt-unprod
2×+-commutative sqrt-pow1 pow-prod-down
1×distribute-rgt-in pow-to-exp associate-+l+ associate-+r+ distribute-lft-in pow1/2 associate-*l* pow-exp sqrt-prod *-commutative
Counts
4 → 253
Calls
4 calls:
24.7s
(* (* (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (sqrt (* PI 2.0))) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))) (/ 771.3234287776531 (- 3.0 z))))))
272.0ms
(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))))
1.0ms
(sqrt (* PI 2.0))
103.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

series618.0ms

Counts
4 → 10
Calls
4 calls:
486.0ms
(* (* (pow (+ 0.5 (- 7.0 z)) (- 0.5 z)) (sqrt (* PI 2.0))) (+ (+ (/ 12.507343278686905 (- 5.0 z)) (/ -176.6150291621406 (- 4.0 z))) (+ (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z))) (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))) (/ 771.3234287776531 (- 3.0 z))))))
80.0ms
(+ (/ -0.13857109526572012 (- 6.0 z)) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z))))
0.0ms
(sqrt (* PI 2.0))
52.0ms
(+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -1259.1392167224028 (- 2.0 z)))

simplify1.5s

Counts
263 → 263
Iterations

Useful iterations: 1 (609.0ms)

IterNodesCost
0101050806
1474846874
done500046874

prune4.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
1.0b
(sqrt (* PI 2.0))
1.6b
(pow (/ 12.507343278686905 (- 5.0 z)) 3)
2.6b
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
111×add-sqr-sqrt
106×times-frac
63×add-cube-cbrt
27×swap-sqr
24×distribute-lft-out--
21×unpow-prod-down cube-prod associate-*r* associate-*l* associate-*l/
19×add-exp-log add-cbrt-cube
18×difference-of-squares
16×frac-add
15×pow1 flip3-+ flip-+
12×flip3-- associate-/r/ flip--
9×frac-times
6×div-inv add-log-exp
5×cbrt-undiv associate-*r/ div-exp
4×associate-+l+ prod-exp cbrt-unprod unswap-sqr
3×pow-unpow
2×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 pow-prod-down pow-exp rem-cube-cbrt
1×+-commutative cube-div pow2 cube-mult pow-to-exp pow-pow pow-plus pow1/2 unpow3 sum-log sqrt-prod pow-sqr *-commutative pow-prod-up sqr-pow
Counts
4 → 201
Calls
4 calls:
33.0ms
(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
2.0ms
(sqrt (* PI 2.0))
11.0ms
(pow (/ 12.507343278686905 (- 5.0 z)) 3)
77.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

series210.0ms

Counts
4 → 10
Calls
4 calls:
41.0ms
(* (/ 12.507343278686905 (- 5.0 z)) (/ 12.507343278686905 (- 5.0 z)))
0.0ms
(sqrt (* PI 2.0))
50.0ms
(pow (/ 12.507343278686905 (- 5.0 z)) 3)
118.0ms
(+ (* (+ (pow 0.9999999999998099 3) (pow (/ 676.5203681218851 (- 1.0 z)) 3)) (- 2.0 z)) (* (+ (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* 0.9999999999998099 0.9999999999998099)) -1259.1392167224028))

simplify506.0ms

Counts
211 → 211
Iterations

Useful iterations: done (492.0ms)

IterNodesCost
04816823
116266045
done50016019

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize151.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (pow (/ 676.5203681218851 (- 1.0 z)) 3) 3)
1.0b
(sqrt (* PI 2.0))
1.6b
(pow (/ 12.507343278686905 (- 5.0 z)) 3)
2.0b
(+ (* (+ (* (pow (/ 676.5203681218851 (- 1.0 z)) 3) (- (pow (/ 676.5203681218851 (- 1.0 z)) 3) (pow 0.9999999999998099 3))) (pow 0.9999999999998099 6)) (* (* (+ 2.0 z) (+ (pow (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) 3) (pow 0.9999999999998099 6))) -1259.1392167224028)) (* (+ (* (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (* 0.9999999999998099 0.9999999999998099) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (* (+ (pow (pow 0.9999999999998099 3) 3) (pow (pow (/ 676.5203681218851 (- 1.0 z)) 3) 3)) (- (* 2.0 2.0) (* z z)))))

rewrite7.6s

Algorithm
rewrite-expression-head
Rules
63868×frac-times
43140×associate-*r/
34616×associate-*l/
33436×frac-add
25122×flip3-- flip--
23641×flip3-+ flip-+
111×unpow-prod-down cube-prod
98×add-sqr-sqrt *-un-lft-identity
90×times-frac
62×add-cube-cbrt
18×distribute-lft-out-- difference-of-squares
12×associate-/r/
11×add-exp-log
8×pow1 distribute-rgt-in associate-+r+ distribute-lft-in pow-exp add-cbrt-cube
6×pow-unpow div-inv add-log-exp
4×cube-mult sub-neg unpow3 sqr-pow
3×cube-div pow-to-exp rem-cube-cbrt
2×pow-pow sqrt-pow1 div-exp
1×cbrt-undiv +-commutative pow1/2 pow-prod-down sum-log sqrt-prod
Counts
4 → 17265
Calls
4 calls:
21.0ms
(pow (pow (/ 676.5203681218851 (- 1.0 z)) 3) 3)
1.0ms
(sqrt (* PI 2.0))
8.0ms
(pow (/ 12.507343278686905 (- 5.0 z)) 3)
1.0s
(+ (* (+ (* (pow (/ 676.5203681218851 (- 1.0 z)) 3) (- (pow (/ 676.5203681218851 (- 1.0 z)) 3) (pow 0.9999999999998099 3))) (pow 0.9999999999998099 6)) (* (* (+ 2.0 z) (+ (pow (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) 3) (pow 0.9999999999998099 6))) -1259.1392167224028)) (* (+ (* (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (* 0.9999999999998099 0.9999999999998099) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (* (+ (pow (pow 0.9999999999998099 3) 3) (pow (pow (/ 676.5203681218851 (- 1.0 z)) 3) 3)) (- (* 2.0 2.0) (* z z)))))

series1.1s

Counts
4 → 10
Calls
4 calls:
75.0ms
(pow (pow (/ 676.5203681218851 (- 1.0 z)) 3) 3)
0.0ms
(sqrt (* PI 2.0))
53.0ms
(pow (/ 12.507343278686905 (- 5.0 z)) 3)
961.0ms
(+ (* (+ (* (pow (/ 676.5203681218851 (- 1.0 z)) 3) (- (pow (/ 676.5203681218851 (- 1.0 z)) 3) (pow 0.9999999999998099 3))) (pow 0.9999999999998099 6)) (* (* (+ 2.0 z) (+ (pow (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) 3) (pow 0.9999999999998099 6))) -1259.1392167224028)) (* (+ (* (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099)) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))) (* (* 0.9999999999998099 0.9999999999998099) (- (* 0.9999999999998099 0.9999999999998099) (* (/ 676.5203681218851 (- 1.0 z)) (- (/ 676.5203681218851 (- 1.0 z)) 0.9999999999998099))))) (* (+ (pow (pow 0.9999999999998099 3) 3) (pow (pow (/ 676.5203681218851 (- 1.0 z)) 3) 3)) (- (* 2.0 2.0) (* z z)))))

simplify44.1s

Counts
17275 → 17275
Iterations

Useful iterations: 0 (15.1s)

IterNodesCost
0637089388120
done637089388120

prune8.5m