Details

Time bar (total: 2.1m)

sample534.0ms

Algorithm
intervals
Results
129.0ms79×body5120valid
109.0ms407×body80nan
94.0ms49×body2560valid
70.0ms204×body80valid
36.0ms27×body1280valid
23.0ms13×body10240exit
19.0ms18×body640valid
5.0ms7×body320valid
2.0ms3×body160valid

simplify1.1s

Counts
1 → 1
Calls
1 calls:
Slowest
1.1s
(* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M)))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 51.1b

localize80.0ms

Local error

Found 4 expressions with local error:

29.2b
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
14.2b
(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
11.7b
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
10.5b
(* (* (/ d D) (/ d D)) (/ c0 h))

rewrite6.5s

Algorithm
rewrite-expression-head
Rules
54×add-cbrt-cube add-exp-log
23×add-sqr-sqrt
22×prod-exp cbrt-unprod
21×*-un-lft-identity
17×associate-*r* add-cube-cbrt
15×cbrt-undiv div-exp
13×times-frac
12×pow1
9×frac-times
8×sqrt-div associate-*l* sqrt-prod
7×fma-def associate-*r/
6×associate-*l/ frac-add add-log-exp
4×expm1-log1p-u flip3-- pow-prod-down insert-posit16 log1p-expm1-u flip--
3×flip3-+ flip-+ unswap-sqr
2×*-commutative div-inv distribute-lft-out difference-of-squares
1×distribute-rgt-in +-commutative rem-sqrt-square sum-log distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 140
Calls
4 calls:
Slowest
4.2s
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
1.8s
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
414.0ms
(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
64.0ms
(* (* (/ d D) (/ d D)) (/ c0 h))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
703.0ms
(* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)))
338.0ms
(+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))
303.0ms
(sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M)))
54.0ms
(* (* (/ d D) (/ d D)) (/ c0 h))

simplify21.1s

Counts
114 → 152
Calls
114 calls:
Slowest
1.2s
(* (* (* (/ c0 (* w 2)) (/ c0 (* w 2))) (/ c0 (* w 2))) (* (* (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))))
722.0ms
(* c0 (+ (* (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3))) w) (* (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) (* (* (/ d D) (/ d D)) (/ c0 h)))))
663.0ms
(+ (* (sqrt (- (pow (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) 3) (pow (* M M) 3))) w) (* (sqrt (+ (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) (+ (* (* M M) (* M M)) (* (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))))) (* (* (/ d D) (/ d D)) (/ c0 h))))
621.0ms
(* (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (/ (* (* c0 c0) c0) (* (* h h) h)))
558.0ms
(* (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (/ (* (* c0 c0) c0) (* (* h h) h)))

prune2.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 27.9b

localize0.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune103.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 27.9b

localize91.0ms

Local error

Found 4 expressions with local error:

29.2b
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
14.2b
(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
11.7b
(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
11.7b
(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
116×add-cbrt-cube add-exp-log
48×cbrt-undiv div-exp
44×add-sqr-sqrt
40×prod-exp cbrt-unprod
32×times-frac
26×associate-*l*
23×*-un-lft-identity add-cube-cbrt
14×associate-*r*
9×pow1
8×sqrt-div unswap-sqr
6×frac-add add-log-exp
4×expm1-log1p-u frac-times flip3-- associate-*l/ associate-*r/ sqrt-prod insert-posit16 log1p-expm1-u div-inv flip--
2×pow-prod-down *-commutative
1×+-commutative rem-sqrt-square sum-log fma-def sqrt-pow1 flip3-+ pow1/2 flip-+ difference-of-squares
Counts
4 → 166
Calls
4 calls:
Slowest
593.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
408.0ms
(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
28.0ms
(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
28.0ms
(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
579.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
452.0ms
(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))
103.0ms
(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
102.0ms
(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))

simplify35.9s

Counts
142 → 178
Calls
142 calls:
Slowest
1.1s
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (/ (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (* (* h h) h)))
1.0s
(* (* (* (/ c0 w) (/ c0 w)) (/ c0 w)) (/ (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (* (* h h) h)))
978.0ms
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (/ (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D))) (* (* h h) h)))
860.0ms
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (/ (* (* (* (/ d D) (/ d D)) (/ d D)) (/ (* (* d d) d) (* (* D D) D))) (* (* h h) h)))
839.0ms
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (/ (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))) (* (* h h) h)))

prune3.2s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 27.5b

localize148.0ms

Local error

Found 4 expressions with local error:

29.2b
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
29.2b
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
29.2b
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
14.2b
(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
20×sqrt-div
18×frac-add
10×flip3-- flip-- add-log-exp
6×add-sqr-sqrt frac-times associate-*l/ associate-*r/
5×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log sqrt-prod insert-posit16 log1p-expm1-u
3×+-commutative sum-log fma-def flip3-+ flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 difference-of-squares
Counts
4 → 82
Calls
4 calls:
Slowest
674.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
651.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
620.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
481.0ms
(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
591.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
574.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
572.0ms
(+ (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))
478.0ms
(sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M)))

simplify18.8s

Counts
62 → 94
Calls
62 calls:
Slowest
1.2s
(* w (sqrt (+ (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))) (+ (* (* M M) (* M M)) (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))))
850.0ms
(* (* w h) (sqrt (+ (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))) (+ (* (* M M) (* M M)) (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))))
829.0ms
(* w (sqrt (+ (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))) (+ (* (* M M) (* M M)) (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))))
757.0ms
(* (* w h) (sqrt (+ (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))) (+ (* (* M M) (* M M)) (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))))
753.0ms
(* (* w h) (sqrt (+ (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))) (+ (* (* M M) (* M M)) (* (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))))))

prune2.2s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 27.5b

regimes1.6s

Accuracy

-5.1% (9.7b remaining)

Error of 34.5b against oracle of 24.8b and baseline of 34.0b

bsearch926.0ms

end0.0ms

sample21.1s

Algorithm
intervals
Results
5.4s2238×body5120valid
4.5s1790×body2560valid
4.4s13318×body80nan
2.1s6892×body80valid
1.4s934×body1280valid
1.3s591×body10240exit
473.0ms432×body640valid
169.0ms205×body320valid
44.0ms95×body160valid