Details

Time bar (total: 1.2m)

sample683.0ms

Algorithm
intervals
Results
414.0ms1143×body80nan
207.0ms392×body80valid

simplify284.0ms

Calls
1 calls:
Slowest
284.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.8b

localize99.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (/ d h) (/ 1 2))
12.9b
(pow (/ d l) (/ 1 2))
12.1b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
6.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
28×prod-exp
14×add-cbrt-cube
10×add-sqr-sqrt pow1 *-un-lft-identity pow-exp add-cube-cbrt
9×pow-to-exp
8×pow-unpow unpow-prod-down
7×associate-*r*
6×cbrt-unprod
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u 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
1×frac-times flip3-- div-exp flip--
Calls
4 calls:
Slowest
37.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
27.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
4.0ms
(pow (/ d h) (/ 1 2))
3.0ms
(pow (/ d l) (/ 1 2))

series743.0ms

Calls
4 calls:
Slowest
426.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
119.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
109.0ms
(pow (/ d h) (/ 1 2))
89.0ms
(pow (/ d l) (/ 1 2))

simplify11.7s

Calls
71 calls:
Slowest
638.0ms
(+ (+ (log (pow (/ d h) (/ 1 2))) (* (log (/ d l)) (/ 1 2))) (log (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))))
628.0ms
(* (* (* (* (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)))))
530.0ms
(* (* (* (* (/ 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)))
521.0ms
(* (* (* (* (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)))))
457.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune2.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 17.5b

localize11.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (/ d h) (/ 1 2))
12.9b
(pow (/ d l) (/ 1 2))
6.6b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)))
6.4b
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
19×prod-exp
9×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
8×pow-to-exp pow1 pow-unpow unpow-prod-down pow-exp
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* cbrt-unprod
2×distribute-rgt-in sub-neg pow-pow distribute-lft-in associate-*l/ associate-*r/
1×clear-num frac-2neg flip3-- associate-*l* pow-prod-down *-commutative flip-- associate-/l* associate-/l/
Calls
4 calls:
Slowest
28.0ms
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)
24.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)))
2.0ms
(pow (/ d h) (/ 1 2))
2.0ms
(pow (/ d l) (/ 1 2))

series676.0ms

Calls
4 calls:
Slowest
380.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)))
111.0ms
(pow (/ d h) (/ 1 2))
99.0ms
(/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)
86.0ms
(pow (/ d l) (/ 1 2))

simplify9.4s

Calls
57 calls:
Slowest
558.0ms
(* (* (* (* (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))))
487.0ms
(* (* (* (* (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))))
458.0ms
(+ (* 1 1) (+ (* (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l) (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l)) (* 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l))))
352.0ms
(+ (+ (log (pow (/ d h) (/ 1 2))) (* (log (/ d l)) (/ 1 2))) (log (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l))))
347.0ms
(+ (+ (* (log (/ d h)) (/ 1 2)) (* (log (/ d l)) (/ 1 2))) (log (- 1 (/ (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) l))))

prune2.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.0b

localize27.0ms

Local error

Found 4 expressions with local error:

13.6b
(pow (/ d h) (/ 1 2))
12.9b
(pow (/ d l) (/ 1 2))
6.7b
(/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
6.6b
(* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1) (- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 pow-unpow unpow-prod-down add-exp-log
6×add-cbrt-cube div-inv
4×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×distribute-rgt-in pow-to-exp sub-neg pow-pow distribute-lft-in pow-exp associate-*r/
1×clear-num frac-2neg flip3-- associate-*l* pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod flip--
Calls
4 calls:
Slowest
37.0ms
(* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1) (- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))))
2.0ms
(pow (/ d h) (/ 1 2))
2.0ms
(pow (/ d l) (/ 1 2))
0.0ms
(/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))

series683.0ms

Calls
4 calls:
Slowest
381.0ms
(* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1) (- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))))
116.0ms
(/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
102.0ms
(pow (/ d h) (/ 1 2))
85.0ms
(pow (/ d l) (/ 1 2))

simplify6.7s

Calls
49 calls:
Slowest
660.0ms
(- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))))
446.0ms
(* (* (* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1) (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1)) (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1)) (* (* (- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))) (- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))))) (- 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))))))
397.0ms
(+ (* 1 1) (+ (* (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))) (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))) (* 1 (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))))))
394.0ms
(* (- (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))) (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1))
355.0ms
(* (* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) 1) (- (/ h (/ l (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2)))))

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.0b

localize22.0ms

Local error

Found 4 expressions with local error:

18.6b
(sqrt (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
18.6b
(sqrt (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
13.6b
(pow (/ d h) (/ 1 2))
12.9b
(pow (/ d l) (/ 1 2))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×pow-unpow unpow-prod-down sqrt-prod
6×pow1 add-exp-log div-inv
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp rem-sqrt-square pow-pow pow1/2 sqrt-div pow-exp
Calls
4 calls:
Slowest
4.0ms
(sqrt (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
2.0ms
(pow (/ d h) (/ 1 2))
2.0ms
(pow (/ d l) (/ 1 2))
1.0ms
(sqrt (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))

series368.0ms

Calls
4 calls:
Slowest
112.0ms
(sqrt (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
95.0ms
(sqrt (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2))
90.0ms
(pow (/ d l) (/ 1 2))
70.0ms
(pow (/ d h) (/ 1 2))

simplify4.0s

Calls
44 calls:
Slowest
391.0ms
(* -1 (/ (* M (* D (sqrt 1/8))) d))
354.0ms
(* -1 (/ (* M (* D (sqrt 1/8))) d))
234.0ms
(exp (* 1/2 (- (log (/ 1 l)) (log (/ 1 d)))))
230.0ms
(exp (* 1/2 (- (log (/ 1 h)) (log (/ 1 d)))))
226.0ms
(exp (* 1/2 (- (log (/ -1 h)) (log (/ -1 d)))))

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.0b

regimes1.3s

Accuracy

46.5% (4.6b remaining)

Error of 21.0b against oracle of 16.5b and baseline of 25.0b

bsearch1.3s

end0.0ms

sample23.3s

Algorithm
intervals
Results
15.6s38694×body80nan
5.9s12835×body80valid