Details

Time bar (total: 47.8s)

sample647.0ms

Algorithm
intervals
Results
427.0ms1220×body80nan
138.0ms401×body80valid

simplify452.0ms

Counts
1 → 1

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize52.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
11.8b
(sqrt (/ d h))
7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
26×sqrt-prod
24×add-sqr-sqrt
21×times-frac
18×*-un-lft-identity add-cube-cbrt
16×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×sqrt-pow1 pow1/2 sqrt-div
1×clear-num associate-/r* frac-2neg fma-udef associate-/l*
Counts
4 → 91
Calls
4 calls:
Slowest
11.0ms
(/ (* M D) (* 2 d))
2.0ms
(sqrt (/ d l))
2.0ms
(sqrt (/ d h))
0.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series503.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
314.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
86.0ms
(sqrt (/ d h))
74.0ms
(sqrt (/ d l))
29.0ms
(/ (* M D) (* 2 d))

simplify644.0ms

Counts
127 → 103

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

localize99.0ms

Local error

Found 4 expressions with local error:

12.3b
(sqrt (/ d l))
7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))
6.8b
(/ (* M D) (* 2 d))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
28×add-cbrt-cube add-exp-log
14×add-sqr-sqrt
13×sqrt-prod
12×times-frac
11×*-un-lft-identity add-cube-cbrt
8×cbrt-undiv div-exp prod-exp cbrt-unprod
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×rem-sqrt-square clear-num associate-/r* frac-2neg associate-/l*
1×sqrt-pow1 pow1/2 sqrt-div fma-udef
Counts
4 → 87
Calls
4 calls:
Slowest
12.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
2.0ms
(sqrt (/ d l))
0.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series886.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
735.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
59.0ms
(sqrt (/ d l))
50.0ms
(/ (* M D) (* 2 d))
42.0ms
(/ (* M D) (* 2 d))

simplify515.0ms

Counts
114 → 99

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.7b

localize122.0ms

Local error

Found 4 expressions with local error:

7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))
6.8b
(/ (* M D) (* 2 d))
6.8b
(* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
46×add-cbrt-cube add-exp-log
22×pow1
21×prod-exp cbrt-unprod
14×associate-*r/
13×pow-prod-down
12×sqrt-div
8×cbrt-undiv div-exp
5×add-sqr-sqrt frac-times *-un-lft-identity associate-*l/ add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
1×associate-*r* *-commutative fma-udef
Counts
4 → 96
Calls
4 calls:
Slowest
503.0ms
(* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
22.0ms
(/ (* M D) (* 2 d))
12.0ms
(/ (* M D) (* 2 d))
1.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h))))))
284.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
39.0ms
(/ (* M D) (* 2 d))
35.0ms
(/ (* M D) (* 2 d))

simplify632.0ms

Counts
111 → 108

prune2.9s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.6b

localize72.0ms

Local error

Found 4 expressions with local error:

7.8b
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
6.8b
(/ (* M D) (* 2 d))
6.8b
(/ (* M D) (* 2 d))
3.3b
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))

rewrite479.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
25×pow1
23×prod-exp cbrt-unprod
15×pow-prod-down
13×associate-*r/
12×sqrt-div
8×cbrt-undiv div-exp
5×frac-times associate-*l/
4×add-sqr-sqrt expm1-log1p-u *-un-lft-identity add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
2×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
1×associate-*r* associate-*l* *-commutative fma-udef
Counts
4 → 97
Calls
4 calls:
Slowest
438.0ms
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
29.0ms
(/ (* M D) (* 2 d))
11.0ms
(/ (* M D) (* 2 d))
0.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(* (* (fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))
319.0ms
(fma (/ h l) (* -1/2 (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) 1)
55.0ms
(/ (* M D) (* 2 d))
32.0ms
(/ (* M D) (* 2 d))

simplify714.0ms

Counts
115 → 109

prune2.7s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.6b

regimes1.8s

Accuracy

-1% (5.3b remaining)

Error of 16.4b against oracle of 11.1b and baseline of 16.3b

bsearch1.0s

end0.0ms

sample24.6s

Algorithm
intervals
Results
15.6s38981×body80nan
5.8s12876×body80valid