Details

Time bar (total: 31.9s)

sample63.0ms

Algorithm
intervals
Results
32.0ms86×body1280valid
10.0ms146×body80valid
3.0ms9×body640valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify40.0ms

Counts
1 → 1
Iterations
IterNodes
done30
430
328
224
119
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
1.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* associate-/l*
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
19.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0ms
(hypot 1.0 x)
9.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(hypot 1.0 x)
15.0ms
(/ 1.0 (hypot 1.0 x))
180.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.5s

Counts
72 → 72
Iterations
IterNodes
done5002
32609
2642
1220
0101

prune490.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.9b

localize117.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
24×pow1
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac associate-*l/
13×add-exp-log add-cbrt-cube
11×flip3-+ flip-+
8×pow-prod-down
6×sqrt-div associate-*r/ associate-/r* associate-/r/ pow-prod-up associate-/l* add-log-exp
4×frac-times sqrt-pow1 associate-*r* frac-add
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- frac-2neg pow1/2 div-exp clear-num flip-- div-inv associate-/l/
1×sub-neg diff-log div-sub associate-*l* sqrt-prod *-commutative
Counts
4 → 108
Calls
4 calls:
11.0ms
(/ 1.0 (hypot 1.0 x))
667.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ (* 1.0 (+ (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) 1.0)) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
185.0ms
(* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
182.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

series1.2s

Counts
4 → 12
Calls
4 calls:
14.0ms
(/ 1.0 (hypot 1.0 x))
665.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (+ (* 1.0 (+ (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) 1.0)) (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
261.0ms
(* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))
310.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

simplify4.7s

Counts
120 → 120
Iterations
IterNodes
done5000
23044
1705
0242

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.9b

localize458.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
1.3b
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.8b
(- (* 1.0 1.0) (* (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) 1.0))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
12×add-log-exp
7×associate-*r/
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip--
3×frac-sub
2×distribute-rgt-out-- associate-*l/ sub-div
1×frac-times distribute-lft-out-- difference-of-squares
Counts
4 → 57
Calls
4 calls:
28.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
183.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
11.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
16.0ms
(- (* 1.0 1.0) (* (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) 1.0))

series824.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
298.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
175.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
197.0ms
(- (* 1.0 1.0) (* (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)) 1.0))

simplify3.0s

Counts
69 → 69
Iterations
IterNodes
done5000
21803
1404
0149

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.9b

localize214.0ms

Local error

Found 4 expressions with local error:

0.9b
(cbrt (* (* (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
1.3b
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
1.3b
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
1.3b
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
30×flip3-- flip--
28×frac-times
26×cbrt-div
14×associate-*l/
10×add-log-exp
8×associate-*r/
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×sub-neg diff-log
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 72
Calls
4 calls:
1.6s
(cbrt (* (* (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
179.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
182.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
169.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

series1.3s

Counts
4 → 12
Calls
4 calls:
323.0ms
(cbrt (* (* (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5)))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))) (- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
307.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
306.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
318.0ms
(- (* (* 1.0 1.0) 1.0) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))

simplify5.3s

Counts
84 → 84
Iterations
IterNodes
done5009
21431
1349
0147

prune890.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.9b

regimes462.0ms

Accuracy

0% (0.0b remaining)

Error of 14.6b against oracle of 14.6b and baseline of 14.6b

bsearch0.0ms

simplify16.0ms

Iterations
IterNodes
done30
130
021

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.6s2828×body1280valid
912.0ms601×body640valid
363.0ms4087×body80valid
82.0ms312×body320valid
25.0ms172×body160valid