Details

Time bar (total: 1.8m)

sample787.0ms

Algorithm
intervals
Results
491.0ms1297×body80nan
222.0ms426×body80valid

simplify383.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
383.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.8b

localize66.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
10.3b
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
8.3b
(sqrt (/ d h))
6.0b
(/ M (/ (* 2 d) D))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
40×add-sqr-sqrt
34×*-un-lft-identity add-cube-cbrt
26×sqrt-prod
13×add-cbrt-cube add-exp-log
7×associate-/r* div-inv
6×pow1
5×cbrt-undiv div-exp
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×sqrt-pow1 pow1/2 sqrt-div
1×clear-num frac-2neg prod-exp associate-/r/ cbrt-unprod fma-udef
Counts
4 → 118
Calls
4 calls:
Slowest
8.0ms
(/ M (/ (* 2 d) D))
3.0ms
(sqrt (/ d l))
3.0ms
(sqrt (/ d h))
0.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)

series520.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
338.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
69.0ms
(sqrt (/ d h))
58.0ms
(sqrt (/ d l))
55.0ms
(/ M (/ (* 2 d) D))

simplify4.5s

Counts
103 → 130
Calls
103 calls:
Slowest
585.0ms
(/ (* (* M M) M) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* D D) D)))
308.0ms
(/ (* (* M M) M) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* D D) D)))
263.0ms
(- (log M) (- (+ (log 2) (log d)) (log D)))
238.0ms
(- 1 (* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (* l (pow d 2)))))
212.0ms
(- (log M) (log (/ (* 2 d) D)))

prune2.5s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.9b

localize84.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
10.3b
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
6.0b
(/ M (/ (* 2 d) D))
6.0b
(/ M (/ (* 2 d) D))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
46×add-sqr-sqrt
43×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube add-exp-log
14×associate-/r*
13×sqrt-prod
11×div-inv
10×cbrt-undiv div-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg prod-exp associate-/r/ cbrt-unprod
1×sqrt-pow1 pow1/2 sqrt-div fma-udef
Counts
4 → 141
Calls
4 calls:
Slowest
16.0ms
(/ M (/ (* 2 d) D))
15.0ms
(/ M (/ (* 2 d) D))
5.0ms
(sqrt (/ d l))
1.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)

series528.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
387.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
55.0ms
(sqrt (/ d l))
51.0ms
(/ M (/ (* 2 d) D))
35.0ms
(/ M (/ (* 2 d) D))

simplify7.9s

Counts
143 → 153
Calls
143 calls:
Slowest
350.0ms
(/ (* (* M M) M) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* D D) D)))
319.0ms
(- 1 (* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (* l (pow d 2)))))
305.0ms
(/ (* (* M M) M) (/ (* (* (* 2 d) (* 2 d)) (* 2 d)) (* (* D D) D)))
275.0ms
(/ (* (* M M) M) (/ (* (* (* 2 2) 2) (* (* d d) d)) (* (* D D) D)))
255.0ms
(- (log M) (- (+ (log 2) (log d)) (log D)))

prune3.7s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.4b

localize81.0ms

Local error

Found 4 expressions with local error:

10.3b
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
6.0b
(/ M (/ (* 2 d) D))
6.0b
(/ M (/ (* 2 d) D))
4.6b
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
40×add-cbrt-cube add-exp-log
37×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
22×pow1
15×prod-exp cbrt-unprod
14×associate-/r*
13×pow-prod-down
10×cbrt-undiv div-exp div-inv
8×associate-*r/
6×associate-/l*
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×clear-num frac-2neg associate-/r/
1×frac-times associate-*r* associate-*l/ *-commutative fma-udef
Counts
4 → 146
Calls
4 calls:
Slowest
189.0ms
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
14.0ms
(/ M (/ (* 2 d) D))
9.0ms
(/ M (/ (* 2 d) D))
0.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
354.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
52.0ms
(/ M (/ (* 2 d) D))
50.0ms
(/ M (/ (* 2 d) D))

simplify14.8s

Counts
147 → 158
Calls
147 calls:
Slowest
1.1s
(* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))))
1.1s
(* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (fabs (cbrt d))) (fabs (cbrt d))) (* (* (sqrt (/ (cbrt d) l)) (sqrt (/ (cbrt d) l))) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (sqrt (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))))))
954.0ms
(* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (fabs (cbrt d))) (fabs (cbrt d))) (* (* (sqrt (/ (cbrt d) l)) (sqrt (/ (cbrt d) l))) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))))
896.0ms
(* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))))
855.0ms
(* (* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (* (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l)))) (* (* (* (fabs (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h)))) (fabs (/ (cbrt d) (cbrt h)))) (* (* (sqrt (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))))))

prune4.6s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 9.1b

localize82.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* (/ (* M D) d) (/ (* M D) d)) h)
5.6b
(/ (* (* (/ (* M D) d) (/ (* M D) d)) h) l)
4.6b
(* (fma (/ (* (* (/ (* M D) d) (/ (* M D) d)) h) l) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
3.9b
(/ (* M D) d)

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
133×add-cbrt-cube add-exp-log
64×prod-exp cbrt-unprod
37×cbrt-undiv div-exp
27×pow1
16×pow-prod-down
11×add-sqr-sqrt
10×*-un-lft-identity associate-*r/ add-cube-cbrt
9×associate-*l/
6×associate-/r* times-frac
4×expm1-log1p-u sqrt-div associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×frac-times associate-/l/
2×clear-num frac-2neg *-commutative div-inv associate-/l*
1×unswap-sqr
Counts
4 → 143
Calls
4 calls:
Slowest
174.0ms
(* (fma (/ (* (* (/ (* M D) d) (/ (* M D) d)) h) l) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
143.0ms
(/ (* (* (/ (* M D) d) (/ (* M D) d)) h) l)
115.0ms
(* (* (/ (* M D) d) (/ (* M D) d)) h)
9.0ms
(/ (* M D) d)

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(* (fma (/ (* (* (/ (* M D) d) (/ (* M D) d)) h) l) -1/8 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
97.0ms
(* (* (/ (* M D) d) (/ (* M D) d)) h)
94.0ms
(/ (* (* (/ (* M D) d) (/ (* M D) d)) h) l)
29.0ms
(/ (* M D) d)

simplify37.1s

Counts
109 → 155
Calls
109 calls:
Slowest
1.5s
(/ (* (* (* (* (/ (* M D) d) (/ (* M D) d)) (/ (* M D) d)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d))) (* (* h h) h)) (* (* l l) l))
1.4s
(/ (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d))) (* (* h h) h)) (* (* l l) l))
1.4s
(/ (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* d d) d)) (* (* (/ (* M D) d) (/ (* M D) d)) (/ (* M D) d))) (* (* h h) h)) (* (* l l) l))
1.4s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* d d) d))) (* (* h h) h))
1.3s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* d d) d)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* d d) d))) (* (* h h) h))

prune3.4s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 6.5b

regimes2.0s

Accuracy

0% (4.4b remaining)

Error of 12.9b against oracle of 8.5b and baseline of 12.9b

bsearch8.0ms

end0.0ms

sample23.3s

Algorithm
intervals
Results
15.8s38190×body80nan
5.2s12604×body80valid