Details

sample103.0ms

Algorithm

intervals

Results

56.0ms	304×	body	80	valid
19.0ms	109×	body	80	nan

simplify163.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

163.0ms

(* w0 (sqrt (- 1 (* (pow (/ (* M D) (* 2 d)) 2) (/ h l)))))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize29.0ms

Local error

Found 4 expressions with local error:

9.6b	(* (/ h l) (/ (* M D) (* 2 d)))
5.6b	(/ (* M D) (* 2 d))
5.6b	(/ (* M D) (* 2 d))
4.9b	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
26×	`prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
19×	`add-sqr-sqrt`
13×	`-un-lft-identity` `times-frac` `associate-l*` `add-cube-cbrt`
7×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l` `unswap-sqr`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 121

Calls

4 calls:

Slowest

31.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
22.0ms	(/ (* M D) (* 2 d))
21.0ms	(/ (* M D) (* 2 d))
11.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series359.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
91.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
39.0ms	(/ (* M D) (* 2 d))
36.0ms	(/ (* M D) (* 2 d))

simplify25.3s

Counts

84 → 133

Calls

84 calls:

Slowest

1.4s	(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.4s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s	(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.3s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize57.0ms

Local error

Found 4 expressions with local error:

6.1b	(/ (* h (/ (* M D) (* 2 d))) l)
5.6b	(/ (* M D) (* 2 d))
5.6b	(/ (* M D) (* 2 d))
5.1b	(* h (/ (* M D) (* 2 d)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-cbrt-cube` `add-exp-log`
26×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `times-frac`
5×	`associate-/r` `associate-r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `associate-/l*`
2×	`associate-*r/`
1×	`pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 113

Calls

4 calls:

Slowest

22.0ms	(* h (/ (* M D) (* 2 d)))
21.0ms	(/ (* M D) (* 2 d))
20.0ms	(/ (* h (/ (* M D) (* 2 d))) l)
17.0ms	(/ (* M D) (* 2 d))

series255.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(/ (* h (/ (* M D) (* 2 d))) l)
63.0ms	(* h (/ (* M D) (* 2 d)))
44.0ms	(/ (* M D) (* 2 d))
33.0ms	(/ (* M D) (* 2 d))

simplify25.1s

Counts

74 → 125

Calls

74 calls:

Slowest

1.9s	(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.8s	(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.5s	(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.3s	(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.0s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize34.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ l (/ (* M D) (* 2 d)))
5.6b	(/ (* M D) (* 2 d))
5.6b	(/ (* M D) (* 2 d))
4.9b	(sqrt (- 1 (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-cbrt-cube` `add-exp-log`
21×	`times-frac`
17×	`cbrt-undiv` `div-exp`
16×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`prod-exp` `cbrt-unprod`
7×	`associate-/r*` `div-inv`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `flip--`

Counts

4 → 113

Calls

4 calls:

Slowest

19.0ms	(/ (* M D) (* 2 d))
13.0ms	(/ (* M D) (* 2 d))
10.0ms	(/ l (/ (* M D) (* 2 d)))
9.0ms	(sqrt (- 1 (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

169.0ms	(sqrt (- 1 (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
85.0ms	(/ l (/ (* M D) (* 2 d)))
51.0ms	(/ (* M D) (* 2 d))
47.0ms	(/ (* M D) (* 2 d))

simplify18.7s

Counts

87 → 125

Calls

87 calls:

Slowest

1.3s	(/ (* (* l l) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
933.0ms	(/ (* (* l l) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
879.0ms	(/ (* (* l l) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
843.0ms	(/ (* (* l l) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
796.0ms	(sqrt (- (pow 1 3) (pow (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d))) 3)))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize47.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ l (/ (* M D) (* 2 d)))
6.9b	(/ l (/ (* M D) (* 2 d)))
6.9b	(/ l (/ (* M D) (* 2 d)))
6.3b	(cbrt (- 1 (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-cbrt-cube` `add-exp-log`
57×	`times-frac`
35×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`cbrt-undiv` `div-exp`
15×	`associate-/r*` `div-inv`
12×	`prod-exp` `cbrt-unprod`
9×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `clear-num` `frac-2neg` `associate-/r/`
2×	`cbrt-div`
1×	`flip3--` `pow1/3` `flip--`

Counts

4 → 157

Calls

4 calls:

Slowest

16.0ms	(/ l (/ (* M D) (* 2 d)))
15.0ms	(/ l (/ (* M D) (* 2 d)))
13.0ms	(/ l (/ (* M D) (* 2 d)))
5.0ms	(cbrt (- 1 (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))

series654.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

412.0ms	(cbrt (- 1 (* (/ h (/ l (/ (* M D) (* 2 d)))) (/ (* M D) (* 2 d)))))
88.0ms	(/ l (/ (* M D) (* 2 d)))
83.0ms	(/ l (/ (* M D) (* 2 d)))
71.0ms	(/ l (/ (* M D) (* 2 d)))

simplify33.3s

Counts

161 → 169

Calls

161 calls:

Slowest

1.0s	(/ (* (* l l) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.0s	(/ (* (* l l) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
975.0ms	(/ (* (* l l) l) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))))
974.0ms	(/ (* (* l l) l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
948.0ms	(/ (* (* l l) l) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune3.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.8b

regimes1.4s

Accuracy

0% (0.7b remaining)

Error of 8.4b against oracle of 7.7b and baseline of 8.4b

bsearch6.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.3s	9390×	body	80	valid
748.0ms	3105×	body	80	nan