Details

Time bar (total: 29.0s)

sample124.0ms

Algorithm
intervals
Results
56.0ms229×body80nan
43.0ms256×body80valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done2036
52036
41057
3256
289
134
016

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (fma -6 (* v v) 2)))
0.0b
(/ (/ 4/3 PI) (- 1 (* v v)))
1.0b
(/ 4/3 PI)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
1324×times-frac
659×add-sqr-sqrt *-un-lft-identity
554×add-cube-cbrt
216×sqrt-prod
210×difference-of-squares
87×associate-/l*
51×div-inv
19×add-cbrt-cube add-exp-log
16×associate-/r/
14×associate-/r*
10×cbrt-undiv div-exp
8×flip3-- flip--
3×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
2×associate-/l/
Counts
3 → 656
Calls
3 calls:
41.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (fma -6 (* v v) 2)))
21.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
7.0ms
(/ 4/3 PI)

series659.0ms

Counts
3 → 7
Calls
3 calls:
543.0ms
(/ (/ (/ 4/3 PI) (- 1 (* v v))) (sqrt (fma -6 (* v v) 2)))
116.0ms
(/ (/ 4/3 PI) (- 1 (* v v)))
0.0ms
(/ 4/3 PI)

simplify2.0s

Counts
663 → 663
Iterations
IterNodes
done2001
12001
01031

prune4.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 4/3 (+ 1 v)) (/ (/ (/ 1 PI) (- 1 v)) (sqrt (fma -6 (* v v) 2))))
0.0b
(/ 4/3 (+ 1 v))
0.0b
(/ (/ 1 PI) (- 1 v))
0.0b
(/ (/ (/ 1 PI) (- 1 v)) (sqrt (fma -6 (* v v) 2)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
2934×times-frac
1777×add-sqr-sqrt
1718×*-un-lft-identity
1151×add-cube-cbrt
515×sqrt-prod
508×associate-*r*
366×difference-of-squares
183×distribute-lft-out--
103×div-inv
100×associate-/l*
80×add-exp-log
52×add-cbrt-cube
46×div-exp
32×associate-/r/
26×cbrt-undiv
18×associate-*l* unswap-sqr
16×associate-/r*
14×flip3-- flip--
12×prod-exp
8×cbrt-unprod
7×distribute-lft-out
6×pow1
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×flip3-+ flip-+ associate-/l/
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 1350
Calls
4 calls:
69.0ms
(* (/ 4/3 (+ 1 v)) (/ (/ (/ 1 PI) (- 1 v)) (sqrt (fma -6 (* v v) 2))))
7.0ms
(/ 4/3 (+ 1 v))
21.0ms
(/ (/ 1 PI) (- 1 v))
41.0ms
(/ (/ (/ 1 PI) (- 1 v)) (sqrt (fma -6 (* v v) 2)))

series882.0ms

Counts
4 → 12
Calls
4 calls:
601.0ms
(* (/ 4/3 (+ 1 v)) (/ (/ (/ 1 PI) (- 1 v)) (sqrt (fma -6 (* v v) 2))))
27.0ms
(/ 4/3 (+ 1 v))
84.0ms
(/ (/ 1 PI) (- 1 v))
170.0ms
(/ (/ (/ 1 PI) (- 1 v)) (sqrt (fma -6 (* v v) 2)))

simplify2.8s

Counts
1362 → 1362
Iterations
IterNodes
done2001
12001
01425

prune7.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))
0.0b
(/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (fma -6 (* v v) 2)))
0.0b
(/ (/ 4/3 PI) (sqrt (- 1 (* v v))))
1.0b
(/ 4/3 PI)

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
450×times-frac
325×add-sqr-sqrt
245×*-un-lft-identity
205×add-cube-cbrt
176×sqrt-prod
110×associate-*r*
103×add-exp-log
61×add-cbrt-cube
60×difference-of-squares
53×div-exp
30×associate-*l*
29×cbrt-undiv
25×unswap-sqr
24×prod-exp
22×div-inv
17×associate-/r* associate-/l*
12×cbrt-unprod
6×pow1 rec-exp sqrt-div 1-exp associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp associate-/l/
3×clear-num frac-2neg flip3-- flip--
2×frac-times associate-*l/ associate-*r/
1×pow-prod-down *-commutative
Counts
4 → 422
Calls
4 calls:
45.0ms
(* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))
47.0ms
(/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (fma -6 (* v v) 2)))
23.0ms
(/ (/ 4/3 PI) (sqrt (- 1 (* v v))))
8.0ms
(/ 4/3 PI)

series1.0s

Counts
4 → 10
Calls
4 calls:
162.0ms
(* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v)))))
587.0ms
(/ (* (/ 1 (sqrt (- 1 (* v v)))) (/ (/ 4/3 PI) (sqrt (- 1 (* v v))))) (sqrt (fma -6 (* v v) 2)))
286.0ms
(/ (/ 4/3 PI) (sqrt (- 1 (* v v))))
0.0ms
(/ 4/3 PI)

simplify2.0s

Counts
432 → 432
Iterations
IterNodes
done2002
22002
11984
0645

prune2.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done20
120
016

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.7s8155×body80nan
1.3s8000×body80valid