Details

Time bar (total: 17.3s)

sample219.0ms

Algorithm
intervals
Results
81.0ms97×body2560valid
53.0ms89×body1280valid
38.0ms31×body640valid
22.0ms241×body80nan
6.0ms15×body320valid
3.0ms16×body160valid
1.0ms8×body80valid

simplify473.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
0.2b
(* 5 (* v v))
0.0b
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
0.0b
(- (* v v) 1)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
11×add-cbrt-cube add-exp-log
10×difference-of-squares
9×pow1
6×associate-/r* add-log-exp
5×difference-of-sqr-1
4×insert-posit16
3×flip3-- associate-*l* pow-prod-down prod-exp cbrt-unprod flip-- associate-/l*
2×associate-/r/ associate-/l/
1×acos-asin cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp associate-*r* *-commutative div-inv unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
29.0ms
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
14.0ms
(- (* v v) 1)
14.0ms
(* 5 (* v v))
1.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(/ (- 1 (* 5 (* v v))) (- (* v v) 1))
51.0ms
(* 5 (* v v))
44.0ms
(- (* v v) 1)
6.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify438.0ms

Counts
128 → 102

prune832.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(acos (+ (- (* 4 (* v v)) 1) (* (* v v) (* 4 (* v v)))))
0.1b
(* (* v v) (* 4 (* v v)))
0.0b
(* 4 (* v v))
0.0b
(* 4 (* v v))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
35×pow1 add-cbrt-cube add-exp-log
21×pow-prod-down prod-exp cbrt-unprod
8×add-sqr-sqrt
7×associate-*l*
6×*-un-lft-identity add-cube-cbrt
4×insert-posit16 add-log-exp
3×associate-*r* *-commutative
2×unswap-sqr
1×acos-asin
Counts
4 → 78
Calls
4 calls:
Slowest
80.0ms
(* (* v v) (* 4 (* v v)))
33.0ms
(acos (+ (- (* 4 (* v v)) 1) (* (* v v) (* 4 (* v v)))))
18.0ms
(* 4 (* v v))
15.0ms
(* 4 (* v v))

series129.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
49.0ms
(* (* v v) (* 4 (* v v)))
48.0ms
(* 4 (* v v))
28.0ms
(* 4 (* v v))
4.0ms
(acos (+ (- (* 4 (* v v)) 1) (* (* v v) (* 4 (* v v)))))

simplify710.0ms

Counts
90 → 90

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
1.0b
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0b
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
0.7b
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

rewrite21.0ms

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×insert-posit16 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 → 87
Calls
4 calls:
Slowest
17.0ms
(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
1.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))
1.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
22.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
20.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
4.0ms
(* (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))) (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))
3.0ms
(acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))

simplify685.0ms

Counts
111 → 99

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize73.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))))
1.0b
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0b
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
1.0b
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
451×sqrt-pow1
342×pow1
244×pow-prod-up
227×pow1/2
102×pow-sqr
71×pow-prod-down
18×pow-plus
16×add-cbrt-cube add-exp-log
13×pow2
10×add-sqr-sqrt
9×sqrt-prod
8×prod-exp cbrt-unprod
7×*-un-lft-identity add-cube-cbrt
5×sqrt-unprod
4×insert-posit16 add-log-exp
3×rem-sqrt-square
1×rem-square-sqrt swap-sqr associate-*r* associate-*l* *-commutative unswap-sqr
Counts
4 → 220
Calls
4 calls:
Slowest
97.0ms
(* (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))))
2.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
2.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
2.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
24.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
16.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
16.0ms
(sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))
9.0ms
(* (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))))

simplify847.0ms

Counts
234 → 232

prune2.3s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes246.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch2.0ms

end0.0ms

sample7.6s

Algorithm
intervals
Results
3.2s2992×body2560valid
2.1s2546×body1280valid
944.0ms8073×body80nan
658.0ms1263×body640valid
256.0ms589×body320valid
96.0ms410×body160valid
25.0ms200×body80valid