Details

Time bar (total: 20.3s)

sample61.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
17.0ms238×body80nan

simplify2.9s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01928
14428
216328
381928
4401628
done500028

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.2b
(* PI t)
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
0.5b
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
18×associate-*r/
16×pow1
13×add-sqr-sqrt prod-exp cbrt-unprod
10×add-cube-cbrt *-un-lft-identity
8×flip3-- sqrt-div associate-*r* associate-/r/ flip--
7×associate-*l* pow-prod-down
4×cbrt-undiv frac-times div-exp add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-*l/ associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 94
Calls
4 calls:
34.0ms
(* 5.0 (* v v))
7.0ms
(* PI t)
209.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
92.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
35.0ms
(* 5.0 (* v v))
37.0ms
(* PI t)
883.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v))))
334.0ms
(* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))

simplify869.0ms

Counts
106 → 106
Iterations

Useful iterations: done (863.0ms)

IterNodesCost
02502389
17822250
done50001948

prune490.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (pow v 4) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
3.4b
(/ (pow v 4) (* t (* (sqrt 2.0) (* (pow (sqrt 1.0) 3) PI))))
4.0b
(/ (* v v) t)
4.1b
(/ (pow v 2) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
148×add-exp-log
73×prod-exp
51×add-cbrt-cube
44×div-exp
25×times-frac
23×associate-/l*
19×cbrt-unprod
18×add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
17×pow-to-exp pow-exp
14×cbrt-undiv
6×associate-/r* sqr-pow
4×pow1 frac-2neg clear-num div-inv add-log-exp
2×unpow2
Counts
4 → 152
Calls
4 calls:
75.0ms
(/ (pow v 4) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
93.0ms
(/ (pow v 4) (* t (* (sqrt 2.0) (* (pow (sqrt 1.0) 3) PI))))
19.0ms
(/ (* v v) t)
78.0ms
(/ (pow v 2) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))

series1.1s

Counts
4 → 12
Calls
4 calls:
306.0ms
(/ (pow v 4) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))
470.0ms
(/ (pow v 4) (* t (* (sqrt 2.0) (* (pow (sqrt 1.0) 3) PI))))
21.0ms
(/ (* v v) t)
319.0ms
(/ (pow v 2) (* t (* (sqrt 2.0) (* (sqrt 1.0) PI))))

simplify575.0ms

Counts
164 → 164
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
02662870
17592568
done50002311

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 5.0 (* v v))
0.3b
(/ (- 1.0 (* 5.0 (* v v))) (* (* (- (* 1.0 1.0) (pow v 4)) PI) (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2)))))))))
0.4b
(* (* (- (* 1.0 1.0) (pow v 4)) PI) (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2))))))))
0.4b
(* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2)))))))

rewrite631.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log add-cbrt-cube
32×associate-*r/
23×pow1
20×prod-exp cbrt-unprod
16×associate-*l/
14×flip3-- sqrt-div flip--
12×add-sqr-sqrt pow-prod-down
9×add-cube-cbrt *-un-lft-identity
8×frac-times associate-/r/
7×associate-*l*
6×associate-*r*
5×cbrt-undiv div-exp
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×associate-/l/ unswap-sqr
1×frac-2neg div-sub clear-num associate-/r* sqrt-prod div-inv
Counts
4 → 108
Calls
4 calls:
17.0ms
(* 5.0 (* v v))
253.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (- (* 1.0 1.0) (pow v 4)) PI) (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2)))))))))
284.0ms
(* (* (- (* 1.0 1.0) (pow v 4)) PI) (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2))))))))
70.0ms
(* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2)))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
48.0ms
(* 5.0 (* v v))
645.0ms
(/ (- 1.0 (* 5.0 (* v v))) (* (* (- (* 1.0 1.0) (pow v 4)) PI) (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2)))))))))
295.0ms
(* (* (- (* 1.0 1.0) (pow v 4)) PI) (* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2))))))))
186.0ms
(* t (sqrt (* 2.0 (- (* 1.0 1.0) (* (* 3.0 3.0) (pow v (* 2 2)))))))

simplify565.0ms

Counts
120 → 120
Iterations

Useful iterations: done (555.0ms)

IterNodesCost
02514259
17913682
done50003116

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* v v))
0.2b
(* 5.0 (* v v))
0.4b
(/ (/ 1 (* (- (* 1.0 1.0) (pow v 4)) PI)) (* t (sqrt (* (- (* 1.0 1.0) (* (pow v 4) (* 3.0 3.0))) 2.0))))
0.4b
(* t (sqrt (* (- (* 1.0 1.0) (* (pow v 4) (* 3.0 3.0))) 2.0)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log
37×add-cbrt-cube
22×div-exp
20×prod-exp
16×pow1 add-sqr-sqrt
15×times-frac
12×add-cube-cbrt *-un-lft-identity cbrt-unprod
10×cbrt-undiv
9×associate-*l* associate-/l*
8×associate-*l/
7×pow-prod-down
6×associate-*r* associate-/r/
4×rec-exp flip3-- sqrt-div 1-exp associate-*r/ flip-- add-log-exp
3×*-commutative div-inv unswap-sqr
1×frac-2neg clear-num associate-/r* sqrt-prod associate-/l/
Counts
4 → 111
Calls
4 calls:
34.0ms
(* 3.0 (* v v))
27.0ms
(* 5.0 (* v v))
87.0ms
(/ (/ 1 (* (- (* 1.0 1.0) (pow v 4)) PI)) (* t (sqrt (* (- (* 1.0 1.0) (* (pow v 4) (* 3.0 3.0))) 2.0))))
70.0ms
(* t (sqrt (* (- (* 1.0 1.0) (* (pow v 4) (* 3.0 3.0))) 2.0)))

series631.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* 3.0 (* v v))
40.0ms
(* 5.0 (* v v))
327.0ms
(/ (/ 1 (* (- (* 1.0 1.0) (pow v 4)) PI)) (* t (sqrt (* (- (* 1.0 1.0) (* (pow v 4) (* 3.0 3.0))) 2.0))))
219.0ms
(* t (sqrt (* (- (* 1.0 1.0) (* (pow v 4) (* 3.0 3.0))) 2.0)))

simplify2.6s

Counts
123 → 123
Iterations

Useful iterations: 2 (658.0ms)

IterNodesCost
02452861
16742633
238312238
done50002238

prune681.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04268
15868
done5868

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s8000×body80valid
1.1s7921×body80nan