Details

Time bar (total: 30.2s)

sample144.0ms

Algorithm
intervals
Results
53.0ms87×body2560valid
43.0ms97×body1280valid
16.0ms262×body80nan
11.0ms36×body640valid
4.0ms20×body320valid
1.0ms10×body160valid
1.0ms6×body80valid

simplify4.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11914
24214
37714
414614
522214
629714
743614
8104314
done500014

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 27
Calls
2 calls:
26.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series50.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* 5.0 (* v v))
9.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify3.6s

Counts
33 → 33
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
053371
1105368
2262310
3554310
4875310
52155310
done5000310

prune92.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 acos-asin pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 83
Calls
4 calls:
2.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
28.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series97.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
37.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
42.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
10.0ms
(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify3.3s

Counts
95 → 95
Iterations

Useful iterations: done (3.3s)

IterNodesCost
0712646
11141855
22531657
34851576
49861520
done50001475

prune230.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b
(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
63×add-sqr-sqrt
24×associate-*l* unswap-sqr
18×unpow-prod-down cube-prod
16×add-cube-cbrt *-un-lft-identity
9×add-exp-log associate-*r*
7×pow1
6×add-cbrt-cube
4×add-log-exp sqr-pow
3×prod-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×acos-asin cube-mult pow-to-exp pow-plus unpow3 pow-exp *-commutative pow-prod-up cbrt-unprod
Counts
4 → 105
Calls
4 calls:
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
52.0ms
(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

series56.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
6.0ms
(* (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
26.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
19.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))

simplify5.2s

Counts
117 → 117
Iterations

Useful iterations: done (5.2s)

IterNodesCost
0934426
11833102
26582755
338932656
done50002624

prune360.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b
(* (sqrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)) (* (sqrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
51×sqrt-prod
27×associate-*l*
18×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
13×pow1
9×add-exp-log unpow-prod-down cube-prod add-cbrt-cube
7×sqrt-pow1
6×pow1/2
5×pow-prod-down
4×add-log-exp
3×rem-sqrt-square prod-exp pow-prod-up cbrt-unprod
2×sqrt-unprod
1×cube-mult pow-plus unpow3 associate-*r* *-commutative sqr-pow
Counts
4 → 85
Calls
4 calls:
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
2.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
89.0ms
(* (sqrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)) (* (sqrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

series115.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
36.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
32.0ms
(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
12.0ms
(* (sqrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)) (* (sqrt (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3)) (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))

simplify5.7s

Counts
97 → 97
Iterations

Useful iterations: done (5.7s)

IterNodesCost
0933802
12073011
26392200
340622176
done50012134

prune414.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes132.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11014
done1014

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.2s3086×body2560valid
1.3s2446×body1280valid
944.0ms7995×body80nan
525.0ms1234×body640valid
145.0ms604×body320valid
109.0ms423×body160valid
19.0ms207×body80valid