Details

Time bar (total: 4.4m)

sample741.0ms

Algorithm
intervals
Results
494.0ms1410×body80nan
163.0ms409×body80valid

simplify364.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
364.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize73.0ms

Local error

Found 4 expressions with local error:

13.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.5b
(pow (/ d h) (/ 1 2))
12.4b
(pow (/ d l) (/ 1 2))
7.2b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
40×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
5×cbrt-undiv div-inv
4×insert-posit16 add-log-exp
3×associate-*l/ associate-*r/
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 208
Calls
4 calls:
Slowest
62.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
58.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
14.0ms
(pow (/ d h) (/ 1 2))
10.0ms
(pow (/ d l) (/ 1 2))

series688.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
415.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
101.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
87.0ms
(pow (/ d h) (/ 1 2))
85.0ms
(pow (/ d l) (/ 1 2))

simplify41.9s

Counts
182 → 220
Calls
182 calls:
Slowest
918.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
880.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
879.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
713.0ms
(* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d h) (/ 1 2))) (pow (/ d h) (/ 1 2))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
712.0ms
(+ (+ (log (/ 1 2)) (* (- (+ (log M) (log D)) (log (* 2 d))) 2)) (- (log h) (log l)))

prune4.9s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 12.0b

localize89.0ms

Local error

Found 4 expressions with local error:

13.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
12.4b
(pow (/ d l) (/ 1 2))
7.2b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
6.1b
(/ (* M D) (* 2 d))

rewrite694.0ms

Algorithm
rewrite-expression-head
Rules
368×add-exp-log
207×prod-exp
103×div-exp
60×pow-exp
46×add-cbrt-cube
28×times-frac
26×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×cbrt-unprod
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
10×associate-*l/
9×pow1 cbrt-undiv
4×insert-posit16 div-inv add-log-exp
3×frac-times sqrt-div associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- associate-*l* pow-prod-down *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 199
Calls
4 calls:
Slowest
559.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
94.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
20.0ms
(/ (* M D) (* 2 d))
10.0ms
(pow (/ d l) (/ 1 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
144.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
102.0ms
(pow (/ d l) (/ 1 2))
35.0ms
(/ (* M D) (* 2 d))

simplify49.9s

Counts
173 → 211
Calls
173 calls:
Slowest
1.3s
(* (* (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
1.2s
(* (* (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ 1 (* (cbrt h) (cbrt h))))) (sqrt (/ 1 (* (cbrt h) (cbrt h))))) (* (* (pow (/ d (cbrt h)) (/ 1 2)) (pow (/ d (cbrt h)) (/ 1 2))) (pow (/ d (cbrt h)) (/ 1 2)))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
1.2s
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
1.0s
(* (* (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2)))) (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2)))) (* (* (pow (/ d l) (/ 1 2)) (pow (/ d l) (/ 1 2))) (pow (/ d l) (/ 1 2)))) (* (* (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
980.0ms
(* (* (* (* (/ 1 2) (/ 1 2)) (/ 1 2)) (* (* (pow (/ (* M D) (* 2 d)) 2) (pow (/ (* M D) (* 2 d)) 2)) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))

prune5.2s

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 10.5b

localize112.0ms

Local error

Found 4 expressions with local error:

13.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
7.2b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
6.1b
(/ (* M D) (* 2 d))
2.9b
(pow (/ d (cbrt h)) (/ 1 2))

rewrite799.0ms

Algorithm
rewrite-expression-head
Rules
407×add-exp-log
241×prod-exp
104×div-exp
62×pow-exp
55×add-cbrt-cube
37×times-frac
32×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
27×cbrt-unprod
22×unpow-prod-down
19×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow
12×pow1
10×associate-*l/
9×cbrt-prod cbrt-undiv
4×pow-prod-down insert-posit16 div-inv add-log-exp
3×frac-times sqrt-div associate-*r/
2×distribute-rgt-in sub-neg distribute-lft-in flip3-- associate-*l* *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 216
Calls
4 calls:
Slowest
720.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
53.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
13.0ms
(/ (* M D) (* 2 d))
6.0ms
(pow (/ d (cbrt h)) (/ 1 2))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
232.0ms
(pow (/ d (cbrt h)) (/ 1 2))
128.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
50.0ms
(/ (* M D) (* 2 d))

simplify54.0s

Counts
190 → 228
Calls
190 calls:
Slowest
1.1s
(* (* (* (sqrt 1) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (pow 1 3) (pow (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) 3)))
980.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (/ (* (* h h) h) (* (* l l) l)))
850.0ms
(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
833.0ms
(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
821.0ms
(* (* (* (sqrt 1) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (* 1 1) (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)) (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))

prune6.6s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 9.1b

localize130.0ms

Local error

Found 4 expressions with local error:

7.2b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
6.7b
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
6.1b
(/ (* M D) (* d 2))
6.1b
(/ (* M D) (* d 2))

rewrite961.0ms

Algorithm
rewrite-expression-head
Rules
359×add-exp-log
260×add-cbrt-cube
192×prod-exp
114×cbrt-unprod
111×div-exp
101×cbrt-undiv
35×times-frac
32×add-sqr-sqrt
26×associate-*l*
24×*-un-lft-identity
20×pow-exp add-cube-cbrt
11×pow1 associate-*r*
10×pow-to-exp
8×associate-*l/
6×div-inv
4×pow-prod-down insert-posit16 add-log-exp difference-of-squares
3×sqrt-div unswap-sqr
2×distribute-rgt-in frac-times clear-num associate-/r* sub-neg frac-2neg distribute-lft-in flip3-- associate-*r/ *-commutative flip-- associate-/l* sqr-pow
1×distribute-lft-out--
Counts
4 → 202
Calls
4 calls:
Slowest
732.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
183.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
23.0ms
(/ (* M D) (* d 2))
13.0ms
(/ (* M D) (* d 2))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
141.0ms
(* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h)
48.0ms
(/ (* M D) (* d 2))
34.0ms
(/ (* M D) (* d 2))

simplify55.9s

Counts
175 → 214
Calls
175 calls:
Slowest
1.4s
(* (/ (/ (* (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (/ (* M D) (* d 2))) (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (/ (* M D) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) (* (* h h) h))
1.2s
(* (/ (/ (* (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) (* (* h h) h))
907.0ms
(* (/ (* (* (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)) (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)) (* (* l l) l)) (* (* h h) h))
842.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
832.0ms
(* (* (* (sqrt 1) (pow (/ d (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- (pow 1 3) (pow (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1) 3)))

prune6.3s

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 7.1b

regimes3.1s

Accuracy

0% (5.4b remaining)

Error of 12.1b against oracle of 6.6b and baseline of 12.1b

bsearch14.0ms

end0.0ms

sample23.3s

Algorithm
intervals
Results
14.9s37737×body80nan
5.5s12649×body80valid