Details

Time bar (total: 22.5s)

sample124.0ms

Algorithm
intervals
Results
54.0ms99×body2560valid
27.0ms82×body1280valid
11.0ms251×body80nan
9.0ms40×body640valid
4.0ms19×body320valid
1.0ms12×body160valid
0.0ms4×body80valid

simplify554.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
6906
5235
4146
377
242
119
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* v (* v 5.0))) (- (* v v) 1.0))
0.1b
(* v (* v 5.0))
0.5b
(acos (/ (- 1.0 (* v (* v 5.0))) (- (* v v) 1.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
12×times-frac
10×add-cbrt-cube add-exp-log
8×pow1
4×associate-/r* difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×acos-asin cbrt-undiv clear-num frac-2neg div-sub div-exp associate-*r* *-commutative div-inv
Counts
3 → 62
Calls
3 calls:
40.0ms
(/ (- 1.0 (* v (* v 5.0))) (- (* v v) 1.0))
12.0ms
(* v (* v 5.0))
1.0ms
(acos (/ (- 1.0 (* v (* v 5.0))) (- (* v v) 1.0)))

series184.0ms

Counts
3 → 9
Calls
3 calls:
127.0ms
(/ (- 1.0 (* v (* v 5.0))) (- (* v v) 1.0))
48.0ms
(* v (* v 5.0))
8.0ms
(acos (/ (- 1.0 (* v (* v 5.0))) (- (* v v) 1.0)))

simplify969.0ms

Counts
71 → 71
Iterations
IterNodes
done5001
21761
1356
0139

prune325.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* v v) (pow v 4))
0.0b
(* 4.0 (+ (* v v) (pow v 4)))
0.5b
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
3×associate-*r* associate-*l*
2×flip3-+ associate-*r/ flip-+
1×distribute-rgt-in acos-asin +-commutative sum-log distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 41
Calls
3 calls:
9.0ms
(+ (* v v) (pow v 4))
45.0ms
(* 4.0 (+ (* v v) (pow v 4)))
1.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

series229.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(+ (* v v) (pow v 4))
109.0ms
(* 4.0 (+ (* v v) (pow v 4)))
5.0ms
(acos (- (* 4.0 (+ (* v v) (pow v 4))) 1.0))

simplify1.7s

Counts
50 → 50
Iterations
IterNodes
done5000
21442
1218
075

prune305.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.5b
(acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))
1.0b
(sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0)))
1.0b
(sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0)))
1.0b
(* (sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))) (sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 83
Calls
4 calls:
1.0ms
(acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))
1.0ms
(sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0)))
1.0ms
(sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0)))
11.0ms
(* (sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))) (sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))))

series99.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))
40.0ms
(sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0)))
39.0ms
(sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0)))
11.0ms
(* (sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))) (sqrt (acos (- (* 4.0 (* v (+ (pow v 3) v))) 1.0))))

simplify5.1s

Counts
95 → 95
Iterations
IterNodes
done5001
34591
2666
1164
074

prune494.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize83.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))))
1.0b
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))
1.0b
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))
1.0b
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
15.0ms
(* (cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))))
1.0ms
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))
1.0ms
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))
2.0ms
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))

series837.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))) (cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0)))))
194.0ms
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))
167.0ms
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))
229.0ms
(cbrt (acos (/ (- 1.0 (* (* v 5.0) v)) (- (* v v) 1.0))))

simplify5.2s

Counts
85 → 85
Iterations
IterNodes
done5001
33671
2502
1140
062

prune464.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.5b

regimes54.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done12
112
010

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.9s3049×body2560valid
1.1s2440×body1280valid
499.0ms8164×body80nan
457.0ms1214×body640valid
130.0ms629×body320valid
64.0ms451×body160valid
18.0ms217×body80valid