Details

Time bar (total: 5.6s)

sample43.0ms

Algorithm
intervals
Results
24.0ms91×body1280valid
5.0ms134×body80valid
3.0ms17×body640valid
1.0ms9×body320valid
0.0ms5×body160valid

simplify3.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
1.9b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
10.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
12.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series218.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
79.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(/ 1.0 (hypot 1.0 x))
99.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Counts
78 → 78

prune174.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 associate-*r/ associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in div-exp clear-num frac-sub flip-- div-inv
1×+-commutative flip3-+ diff-log sum-log flip-+ distribute-lft-out
Counts
4 → 84
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
15.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series135.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
35.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify138.0ms

Counts
96 → 96

prune275.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 12.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (hypot 1.0 x))
0.2b
(cbrt (hypot 1.0 x))
0.2b
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
1.3b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ (sqrt 1.0) (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))) (/ (sqrt 1.0) (cbrt (hypot 1.0 x))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity associate-*r/
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* frac-sub add-log-exp
4×flip3-- associate--l+ add-cbrt-cube flip-- unswap-sqr
3×sub-neg
2×distribute-rgt-in frac-times distribute-lft-in pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus diff-log prod-exp *-commutative cbrt-unprod
Counts
4 → 84
Calls
4 calls:
1.0ms
(cbrt (hypot 1.0 x))
1.0ms
(cbrt (hypot 1.0 x))
11.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
26.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ (sqrt 1.0) (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))) (/ (sqrt 1.0) (cbrt (hypot 1.0 x))))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(cbrt (hypot 1.0 x))
113.0ms
(cbrt (hypot 1.0 x))
138.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
112.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (* (/ (sqrt 1.0) (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))) (/ (sqrt 1.0) (cbrt (hypot 1.0 x))))))

simplify56.0ms

Counts
96 → 96

prune371.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
0.2b
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
0.2b
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
1.3b
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (* (/ (sqrt 1.0) (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))) (/ (sqrt 1.0) (cbrt (hypot 1.0 x))))) 3))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
48×cbrt-prod
30×*-un-lft-identity
28×add-cube-cbrt
25×pow1
18×pow1/3 swap-sqr associate-*r* associate-*l*
14×associate-*r/
12×cube-div unswap-sqr
10×add-exp-log
6×pow-prod-down pow-sqr pow-prod-up frac-sub add-log-exp
4×flip3-- add-cbrt-cube flip-- difference-of-squares sqr-pow
3×pow2 pow-plus prod-exp *-commutative cbrt-unprod
2×frac-times associate-*l/
1×difference-cubes sub-neg diff-log distribute-lft-out--
Counts
4 → 144
Calls
4 calls:
11.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
11.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
15.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
23.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (* (/ (sqrt 1.0) (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))) (/ (sqrt 1.0) (cbrt (hypot 1.0 x))))) 3))

series612.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
132.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
143.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
203.0ms
(- (pow (* 1.0 (- 1.0 0.5)) 3) (pow (* 0.5 (* (/ (sqrt 1.0) (* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))) (/ (sqrt 1.0) (cbrt (hypot 1.0 x))))) 3))

simplify97.0ms

Counts
156 → 156

prune816.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.4b

regimes151.0ms

Accuracy

0% (0.1b remaining)

Error of 15.2b against oracle of 15.1b and baseline of 15.2b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.0s2864×body1280valid
159.0ms4027×body80valid
150.0ms616×body640valid
110.0ms331×body320valid
12.0ms162×body160valid