Details

Time bar (total: 9.2s)

sample30.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
9.0ms274×body80nan

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03210
19110
226310
362010
4113810
5147010
6151010
7151010

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
37×add-exp-log add-cbrt-cube
23×pow1
18×associate-*r/ prod-exp cbrt-unprod
13×flip3-- flip--
12×add-sqr-sqrt sqrt-div pow-prod-down
11×associate-*r*
10×add-cube-cbrt *-un-lft-identity
8×frac-times associate-/r/
5×associate-*l*
4×cbrt-undiv div-exp associate-*l/ add-log-exp
3×times-frac sqrt-prod *-commutative associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in
1×frac-2neg clear-num associate-/r* div-inv difference-of-squares unswap-sqr
Counts
4 → 109
Calls
4 calls:
7.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
12.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms
(* 6.0 (* v v))
13.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series981.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (* 3.0 PI) (- 1.0 (* v v)))
411.0ms
(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
32.0ms
(* 6.0 (* v v))
436.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify112.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08881350
144081176
250021174

prune272.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
0.2b
(* 6.0 (* v v))
1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
40×associate-*r/ associate-/r/
38×add-exp-log add-cbrt-cube
36×cbrt-prod
30×unpow-prod-down flip3-- sqrt-div cube-prod flip--
20×frac-times
18×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
15×times-frac prod-exp cbrt-unprod
10×pow1 associate-*l/
8×cbrt-undiv div-exp
5×pow-exp div-inv rem-cube-cbrt
4×add-log-exp
3×pow-unpow associate-*l* pow-prod-down associate-/l*
2×cube-div cube-mult unpow3 sqr-pow
1×pow-to-exp cbrt-div pow-pow frac-2neg pow1/3 associate-*r* clear-num associate-/r* *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 154
Calls
4 calls:
8.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
9.0ms
(* 6.0 (* v v))
13.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
15.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

series1.8s

Counts
4 → 12
Calls
4 calls:
359.0ms
(cbrt (pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3))
24.0ms
(* 6.0 (* v v))
444.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))
944.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))) 3)

simplify61.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011522676
150022534

prune437.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* v v) 3)
1.0b
(* (pow (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) 3) (pow (* (sqrt (+ 2.0 (* 6.0 (* v v)))) (+ (* (pow v 2) (+ (pow v 2) 1.0)) (* 1.0 1.0))) 3))
1.0b
(pow (* (sqrt (+ 2.0 (* 6.0 (* v v)))) (+ (* (pow v 2) (+ (pow v 2) 1.0)) (* 1.0 1.0))) 3)
1.0b
(pow (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) 3)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
67×prod-exp
46×associate-*r/
43×pow-exp
42×sqrt-div
36×frac-times associate-*l*
35×unpow-prod-down cube-prod
34×cube-div
32×associate-/r/
27×add-sqr-sqrt add-cbrt-cube
24×flip3-- flip--
20×div-exp
18×flip3-+ flip-+
17×add-cube-cbrt *-un-lft-identity
16×pow1
15×associate-*l/
14×pow-to-exp
12×times-frac
11×sqr-pow
9×pow-unpow pow-pow cbrt-unprod rem-cube-cbrt
8×associate-*r* unswap-sqr
5×cube-mult unpow3
4×cbrt-undiv div-inv add-log-exp
3×pow-prod-down
1×pow2 pow-plus pow-sqr *-commutative pow-prod-up
Counts
4 → 219
Calls
4 calls:
4.0ms
(pow (* v v) 3)
29.0ms
(* (pow (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) 3) (pow (* (sqrt (+ 2.0 (* 6.0 (* v v)))) (+ (* (pow v 2) (+ (pow v 2) 1.0)) (* 1.0 1.0))) 3))
15.0ms
(pow (* (sqrt (+ 2.0 (* 6.0 (* v v)))) (+ (* (pow v 2) (+ (pow v 2) 1.0)) (* 1.0 1.0))) 3)
23.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) 3)

series1.8s

Counts
4 → 12
Calls
4 calls:
49.0ms
(pow (* v v) 3)
669.0ms
(* (pow (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) 3) (pow (* (sqrt (+ 2.0 (* 6.0 (* v v)))) (+ (* (pow v 2) (+ (pow v 2) 1.0)) (* 1.0 1.0))) 3))
419.0ms
(pow (* (sqrt (+ 2.0 (* 6.0 (* v v)))) (+ (* (pow v 2) (+ (pow v 2) 1.0)) (* 1.0 1.0))) 3)
667.0ms
(pow (/ 4.0 (* (* (* 3.0 PI) (- (pow 1.0 3) (pow (* v v) 3))) (sqrt (- (* 2.0 2.0) (* (* 6.0 (* v v)) (* 6.0 (* v v))))))) 3)

simplify87.0ms

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015516231
150015953

prune1.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* (* (cbrt (* 6.0 (* v v))) (cbrt (* 6.0 (* v v)))) (cbrt (* 6.0 (* v v))))))))
28.7b
(cbrt (* 6.0 (* v v)))
28.7b
(cbrt (* 6.0 (* v v)))
28.7b
(cbrt (* 6.0 (* v v)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
8×associate-*r/ associate-/r/
6×add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity sqrt-div prod-exp flip-- cbrt-unprod
4×pow1 cbrt-undiv frac-times div-exp add-log-exp
3×cbrt-prod times-frac pow1/3 associate-/l*
2×associate-*l/
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 60
Calls
4 calls:
12.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* (* (cbrt (* 6.0 (* v v))) (cbrt (* 6.0 (* v v)))) (cbrt (* 6.0 (* v v))))))))
5.0ms
(cbrt (* 6.0 (* v v)))
5.0ms
(cbrt (* 6.0 (* v v)))
5.0ms
(cbrt (* 6.0 (* v v)))

series1.1s

Counts
4 → 12
Calls
4 calls:
472.0ms
(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* (* (cbrt (* 6.0 (* v v))) (cbrt (* 6.0 (* v v)))) (cbrt (* 6.0 (* v v))))))))
216.0ms
(cbrt (* 6.0 (* v v)))
224.0ms
(cbrt (* 6.0 (* v v)))
223.0ms
(cbrt (* 6.0 (* v v)))

simplify68.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05811134
12669963
25001963

prune201.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04431
14431

end0.0ms

sample737.0ms

Algorithm
intervals
Results
294.0ms8000×body80valid
265.0ms7966×body80nan