Details

Time bar (total: 1.3m)

sample717.0ms

Algorithm
intervals
Results
437.0ms1247×body80nan
189.0ms419×body80valid

simplify495.0ms

Calls
1 calls:
Slowest
495.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize53.0ms

Local error

Found 4 expressions with local error:

12.6b
(sqrt (/ d h))
11.6b
(sqrt (/ d l))
9.4b
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
9.1b
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
198×sqrt-div
145×add-sqr-sqrt
108×associate-*r/
81×frac-times
80×*-un-lft-identity add-cube-cbrt
76×sqrt-prod
66×associate-/r* associate-/l*
62×associate-*r*
50×times-frac
28×unswap-sqr
22×clear-num frac-2neg
19×associate-*l*
11×pow1
9×add-cbrt-cube associate-*l/ add-exp-log
4×expm1-log1p-u rem-sqrt-square insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×sqrt-pow1 pow1/2 *-commutative
1×fma-udef
Calls
4 calls:
Slowest
120.0ms
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h))))
6.0ms
(sqrt (/ d h))
5.0ms
(sqrt (/ d l))
0.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)

series1.1s

Calls
4 calls:
Slowest
554.0ms
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (sqrt (/ d h))))
374.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
83.0ms
(sqrt (/ d h))
76.0ms
(sqrt (/ d l))

simplify7.3s

Calls
235 calls:
Slowest
517.0ms
(* (* (* (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)) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ d l))) (* (* (sqrt (/ d h)) (sqrt (/ d h))) (sqrt (/ d h)))))
323.0ms
(* (* (* (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)) (* (* (* (sqrt (/ d l)) (sqrt (/ d h))) (* (sqrt (/ d l)) (sqrt (/ d h)))) (* (sqrt (/ d l)) (sqrt (/ d h)))))
301.0ms
(- 1 (* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (* l (pow d 2)))))
292.0ms
(- 1 (* 1/8 (/ (* (pow M 2) (* (pow D 2) h)) (* l (pow d 2)))))
196.0ms
(* (sqrt (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)) (* (sqrt (/ (sqrt d) (sqrt l))) (sqrt (sqrt (/ d h)))))

prune5.1s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 12.3b

localize46.0ms

Local error

Found 4 expressions with local error:

11.6b
(sqrt (/ d l))
9.4b
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
9.1b
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
3.9b
(/ M (/ (* 2 d) D))

rewrite351.0ms

Algorithm
rewrite-expression-head
Rules
482×add-sqr-sqrt
361×times-frac
324×associate-*r/
303×sqrt-div
256×*-un-lft-identity add-cube-cbrt
238×associate-*r*
154×associate-/r*
135×frac-times
129×sqrt-prod
126×associate-/l*
124×cbrt-prod
119×unswap-sqr
61×associate-*l*
29×clear-num frac-2neg
22×add-cbrt-cube add-exp-log
18×associate-/r/
16×*-commutative
14×pow1
9×associate-*l/
8×div-inv
7×prod-exp cbrt-unprod
6×pow-prod-down
5×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square
1×sqrt-pow1 pow1/2 fma-udef
Calls
4 calls:
Slowest
285.0ms
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
25.0ms
(/ M (/ (* 2 d) D))
6.0ms
(sqrt (/ d l))
0.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)

series1.3s

Calls
4 calls:
Slowest
816.0ms
(* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
388.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
60.0ms
(sqrt (/ d l))
53.0ms
(/ M (/ (* 2 d) D))

simplify40.7s

Calls
654 calls:
Slowest
709.0ms
(* (* (* (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)) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ 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)))))))
702.0ms
(* (* (* (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)) (* (* (* (sqrt (/ d l)) (sqrt (/ d l))) (sqrt (/ 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)))))))
605.0ms
(* (* (* (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)) (* (* (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) (* (sqrt (/ d l)) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))))
555.0ms
(/ 1 (/ (* 2 (* (cbrt d) (cbrt d))) (* (cbrt D) (cbrt D))))
536.0ms
(/ (* (cbrt M) (cbrt M)) (/ (* (cbrt (* 2 d)) (cbrt (* 2 d))) (* (cbrt D) (cbrt D))))

prune13.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 12.2b

localize69.0ms

Local error

Found 4 expressions with local error:

9.4b
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
4.2b
(* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))))) (* (sqrt (/ (cbrt d) (cbrt l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
3.9b
(/ M (/ (* 2 d) D))
3.9b
(/ M (/ (* 2 d) D))

rewrite4.1s

Algorithm
rewrite-expression-head
Rules
46226×add-sqr-sqrt
42432×sqrt-div
29637×associate-*r/
29440×cbrt-prod
27585×frac-times
19358×unswap-sqr
18134×associate-/r*
18078×associate-/l*
12847×*-un-lft-identity add-cube-cbrt
9951×sqrt-prod
9317×times-frac
4980×swap-sqr
4457×associate-*r*
4350×associate-*l*
2116×clear-num frac-2neg
1388×*-commutative
927×associate-*l/
43×add-cbrt-cube add-exp-log
36×associate-/r/
25×pow1
17×prod-exp cbrt-unprod
15×pow-prod-down
13×div-inv
10×cbrt-undiv div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
1×fma-udef
Calls
4 calls:
Slowest
867.0ms
(* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))))) (* (sqrt (/ (cbrt d) (cbrt l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
46.0ms
(/ M (/ (* 2 d) D))
16.0ms
(/ M (/ (* 2 d) D))
0.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)

series1.2s

Calls
4 calls:
Slowest
792.0ms
(* (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (sqrt (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))))) (* (sqrt (/ (cbrt d) (cbrt l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
336.0ms
(fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1)
46.0ms
(/ M (/ (* 2 d) D))
38.0ms
(/ M (/ (* 2 d) D))