Details

Time bar (total: 3.2m)

sample654.0ms

Algorithm
intervals
Results
205.0ms490×body80nan
129.0ms65×body5120valid
119.0ms59×body2560valid
62.0ms233×body80valid
34.0ms26×body1280valid
21.0ms10×body10240exit
14.0ms14×body640valid
6.0ms7×body320valid
3.0ms5×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)))))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.9b

localize83.0ms

Local error

Found 4 expressions with local error:

24.6b
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
16.6b
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M)))
11.2b
(* (/ c0 w) (* (/ d D) (/ d D)))
11.2b
(* (/ c0 w) (* (/ d D) (/ d D)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
86×add-cbrt-cube add-exp-log
36×prod-exp cbrt-unprod
26×cbrt-undiv div-exp associate-*l*
24×add-sqr-sqrt
20×*-un-lft-identity times-frac
18×frac-times add-cube-cbrt
17×pow1
16×sqrt-div
14×associate-*r/
10×associate-*l/
8×frac-add
7×flip3-+ pow-prod-down flip-+
6×flip3-- flip-- add-log-exp
4×insert-posit16 unswap-sqr
2×sqrt-pow1 associate-*r* *-commutative div-inv
1×+-commutative sum-log pow1/2 sqrt-prod distribute-lft-out
Counts
4 → 149
Calls
4 calls:
Slowest
42.0ms
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
35.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))
31.0ms
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M)))
26.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
936.0ms
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
700.0ms
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M)))
99.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))
96.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))

simplify27.3s

Counts
133 → 161
Calls
133 calls:
Slowest
1.1s
(+ (* (sqrt (* (- (* M M) (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))) (- (pow (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) 3) (pow M 3)))) h) (* (sqrt (* (- M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (+ (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (+ (* M M) (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))))) (* (/ c0 w) (* (/ d D) (/ d D)))))
761.0ms
(+ (* (sqrt (* (+ (pow M 3) (pow (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) 3)) (- (pow (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) 3) (pow M 3)))) h) (* (sqrt (* (+ (* M M) (- (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (* M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)))) (+ (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (+ (* M M) (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))))) (* (/ c0 w) (* (/ d D) (/ d D)))))
709.0ms
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))))
690.0ms
(+ (* (sqrt (* (+ (pow M 3) (pow (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) 3)) (- (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (* M M)))) h) (* (sqrt (* (+ (* M M) (- (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (* M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)))) (+ (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) M))) (* (/ c0 w) (* (/ d D) (/ d D)))))
606.0ms
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))))

prune3.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 44.8b

localize70.0ms

Local error

Found 4 expressions with local error:

26.1b
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
16.6b
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M)))
11.2b
(* (/ c0 w) (* (/ d D) (/ d D)))
11.2b
(* (/ c0 w) (* (/ d D) (/ d D)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
86×add-cbrt-cube add-exp-log
36×prod-exp cbrt-unprod
26×cbrt-undiv div-exp associate-*l*
24×add-sqr-sqrt
20×*-un-lft-identity times-frac
18×frac-times add-cube-cbrt
17×pow1
16×sqrt-div
14×associate-*r/
10×associate-*l/
8×frac-add
7×flip3-+ pow-prod-down flip-+
6×flip3-- flip-- add-log-exp
4×insert-posit16 unswap-sqr
2×sqrt-pow1 associate-*r* *-commutative div-inv
1×+-commutative sum-log pow1/2 sqrt-prod distribute-lft-out
Counts
4 → 149
Calls
4 calls:
Slowest
56.0ms
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
53.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))
47.0ms
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M)))
26.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.3s
(+ (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))
725.0ms
(sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M)))
116.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))
87.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))

simplify26.2s

Counts
133 → 161
Calls
133 calls:
Slowest
821.0ms
(* (* (* (/ c0 w) (/ c0 w)) (/ c0 w)) (* (* (* (/ d D) (/ d D)) (/ d D)) (/ (* (* d d) d) (* (* D D) D))))
817.0ms
(+ (* (sqrt (* (+ (pow M 3) (pow (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) 3)) (- (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M))) h) (* (sqrt (+ (* M M) (- (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (* M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h))))) (* (/ c0 w) (* (/ d D) (/ d D)))))
721.0ms
(* (/ (* (* c0 c0) c0) (* (* w w) w)) (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D))))
681.0ms
(* (sqrt (* (+ (* M M) (- (* (/ (* (/ c0 w) (* (/ d D) (/ d D))) h) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (* M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)))) (+ (* (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h)) (+ (* M M) (* (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M))))) h)
680.0ms
(+ (* (sqrt (* (+ M (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (- (pow (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) 3) (pow M 3)))) h) (* (sqrt (+ (* (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h)) (+ (* M M) (* (/ (* (* (/ c0 w) (/ d D)) (/ d D)) h) M)))) (* (/ c0 w) (* (/ d D) (/ d D)))))

prune3.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 44.6b

localize66.0ms

Local error

Found 4 expressions with local error:

11.2b
(* (/ c0 w) (* (/ d D) (/ d D)))
7.7b
(/ (* (/ d D) (/ d D)) w)
6.9b
(* (+ (/ c0 (/ h (/ (* (/ d D) (/ d D)) w))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (/ c0 w))
6.7b
(/ (* (/ c0 w) (* (/ d D) (/ d D))) h)

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
121×add-cbrt-cube add-exp-log
47×cbrt-undiv div-exp
42×prod-exp cbrt-unprod
31×add-sqr-sqrt
26×times-frac
25×*-un-lft-identity
23×add-cube-cbrt
17×associate-*l*
14×frac-times associate-*r*
12×associate-*r/
11×pow1
10×associate-*l/ associate-/l/
6×associate-/r*
4×pow-prod-down insert-posit16 div-inv add-log-exp unswap-sqr
2×clear-num frac-2neg flip3-+ frac-add *-commutative flip-+ associate-/l*
1×distribute-lft-out
Counts
4 → 172
Calls
4 calls:
Slowest
116.0ms
(* (+ (/ c0 (/ h (/ (* (/ d D) (/ d D)) w))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (/ c0 w))
60.0ms
(/ (* (/ c0 w) (* (/ d D) (/ d D))) h)
53.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))
14.0ms
(/ (* (/ d D) (/ d D)) w)

series539.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(* (+ (/ c0 (/ h (/ (* (/ d D) (/ d D)) w))) (/ (* (/ c0 w) (* (/ d D) (/ d D))) h)) (/ c0 w))
123.0ms
(* (/ c0 w) (* (/ d D) (/ d D)))
116.0ms
(/ (* (/ c0 w) (* (/ d D) (/ d D))) h)
66.0ms
(/ (* (/ d D) (/ d D)) w)

simplify32.4s

Counts
151 → 184
Calls
151 calls:
Slowest
1.0s
(- (+ (- (log c0) (log w)) (+ (- (log d) (log D)) (log (/ d D)))) (log h))
938.0ms
(/ (* (/ (* (* c0 c0) c0) (* (* w w) w)) (* (* (* (/ d D) (/ d D)) (/ d D)) (/ (* (* d d) d) (* (* D D) D)))) (* (* h h) h))
910.0ms
(/ (* (/ (* (* c0 c0) c0) (* (* w w) w)) (* (/ (* (* d d) d) (* (* D D) D)) (/ (* (* d d) d) (* (* D D) D)))) (* (* h h) h))
865.0ms
(/ (* (/ (* (* c0 c0) c0) (* (* w w) w)) (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D)))) (* (* h h) h))
765.0ms
(/ (* (* (* (/ c0 w) (/ c0 w)) (/ c0 w)) (* (/ (* (* d d) d) (* (* D D) D)) (* (* (/ d D) (/ d D)) (/ d D)))) (* (* h h) h))

prune3.3s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 37.3b

localize37.0ms

Local error

Found 4 expressions with local error:

11.6b
(/ (* d c0) (* w D))
11.6b
(/ (* d c0) (* w D))
8.5b
(/ (* (/ (* d c0) (* w D)) (/ (* d c0) (* w D))) h)
0.2b
(* (/ (* d c0) (* w D)) (/ (* d c0) (* w D)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
315×add-cbrt-cube add-exp-log
138×prod-exp cbrt-unprod
114×cbrt-undiv div-exp
12×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
9×times-frac
7×div-inv
5×associate-/r* swap-sqr associate-*r* associate-*l*
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-/l* associate-/l/
2×frac-times associate-*l/ associate-*r/
1×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 200
Calls
4 calls:
Slowest
77.0ms
(* (/ (* d c0) (* w D)) (/ (* d c0) (* w D)))
50.0ms
(/ (* (/ (* d c0) (* w D)) (/ (* d c0) (* w D))) h)
18.0ms
(/ (* d c0) (* w D))
12.0ms
(/ (* d c0) (* w D))

series257.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
100.0ms
(/ (* (/ (* d c0) (* w D)) (/ (* d c0) (* w D))) h)
82.0ms
(* (/ (* d c0) (* w D)) (/ (* d c0) (* w D)))
45.0ms
(/ (* d c0) (* w D))
30.0ms
(/ (* d c0) (* w D))

simplify1.0m

Counts
177 → 212
Calls
177 calls:
Slowest
3.3s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
3.0s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
2.8s
(/ (* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
2.5s
(/ (* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
2.4s
(* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w D) (* w D)) (* w D))))

prune2.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 32.2b

regimes1.6s

Accuracy

1.7% (9.8b remaining)

Error of 45.6b against oracle of 35.8b and baseline of 45.8b

bsearch1.2s

end0.0ms

sample19.8s

Algorithm
intervals
Results
6.1s2216×body5120valid
4.1s13457×body80nan
3.0s1750×body2560valid
1.9s6929×body80valid
1.5s538×body10240exit
1.3s918×body1280valid
429.0ms451×body640valid
184.0ms219×body320valid
43.0ms103×body160valid