Details

sample120.0ms

Algorithm

intervals

Results

67.0ms	317×	body	80	valid
16.0ms	90×	body	80	nan

simplify195.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

195.0ms

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize27.0ms

Local error

Found 4 expressions with local error:

10.1b	(* (/ h l) (/ (* M D) (* 2 d)))
4.7b	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
4.1b	(/ (* M D) (* 2 d))
4.1b	(/ (* M D) (* 2 d))

rewrite58.0ms

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

29.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
11.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
6.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

175.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
102.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
48.0ms	(/ (* M D) (* 2 d))
35.0ms	(/ (* M D) (* 2 d))

simplify25.5s

Counts

84 → 133

Calls

84 calls:

Slowest

1.6s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.4s	(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
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))))
1.2s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize40.0ms

Local error

Found 4 expressions with local error:

6.8b	(* h (/ (* M D) (* 2 d)))
4.7b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
4.1b	(/ (* M D) (* 2 d))
4.1b	(/ (* M D) (* 2 d))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

Slowest

31.0ms	(* h (/ (* M D) (* 2 d)))
11.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
8.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

401.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
79.0ms	(* h (/ (* M D) (* 2 d)))
49.0ms	(/ (* M D) (* 2 d))
44.0ms	(/ (* M D) (* 2 d))

simplify16.1s

Counts

60 → 110

Calls

60 calls:

Slowest

1.0s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
958.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
886.0ms	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
767.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
756.0ms	(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))

prune1.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.8b

localize74.0ms

Local error

Found 4 expressions with local error:

6.8b	(* h (/ (* M D) (* 2 d)))
6.8b	(* h (/ (* M D) (* 2 d)))
4.7b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
4.7b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-cbrt-cube` `add-exp-log`
18×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
10×	`pow1` `-un-lft-identity` `associate-r*` `add-cube-cbrt`
8×	`cbrt-undiv` `div-exp`
6×	`associate-l` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `times-frac` `flip3--` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `div-inv` `flip--` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

Slowest

28.0ms	(* h (/ (* M D) (* 2 d)))
27.0ms	(* h (/ (* M D) (* 2 d)))
11.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
9.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series961.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

454.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
373.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
71.0ms	(* h (/ (* M D) (* 2 d)))
63.0ms	(* h (/ (* M D) (* 2 d)))

simplify21.3s

Counts

68 → 112

Calls

68 calls:

Slowest

1.2s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.1s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.1s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.1s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.0s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.8b

localize89.0ms

Local error

Found 4 expressions with local error:

6.8b	(* h (/ (* M D) (* 2 d)))
4.7b	(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (* (cbrt h) (/ (* M D) (* 2 d)))) l) (/ (* M D) (* 2 d)))))
4.7b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
4.1b	(/ (* M D) (* 2 d))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

Slowest

42.0ms	(* h (/ (* M D) (* 2 d)))
11.0ms	(/ (* M D) (* 2 d))
5.0ms	(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (* (cbrt h) (/ (* M D) (* 2 d)))) l) (/ (* M D) (* 2 d)))))
5.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series936.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

431.0ms	(sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (* (cbrt h) (/ (* M D) (* 2 d)))) l) (/ (* M D) (* 2 d)))))
383.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
84.0ms	(* h (/ (* M D) (* 2 d)))
38.0ms	(/ (* M D) (* 2 d))

simplify17.3s

Counts

57 → 104

Calls

57 calls:

Slowest

1.2s	(sqrt (- (pow 1 3) (pow (* (/ (* (* (cbrt h) (cbrt h)) (* (cbrt h) (/ (* M D) (* 2 d)))) l) (/ (* M D) (* 2 d))) 3)))
1.2s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.2s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
964.0ms	(sqrt (- (* 1 1) (* (* (/ (* (* (cbrt h) (cbrt h)) (* (cbrt h) (/ (* M D) (* 2 d)))) l) (/ (* M D) (* 2 d))) (* (/ (* (* (cbrt h) (cbrt h)) (* (cbrt h) (/ (* M D) (* 2 d)))) l) (/ (* M D) (* 2 d))))))
960.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.6s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.8b

regimes1.4s

Accuracy

0% (0.5b remaining)

Error of 8.2b against oracle of 7.7b and baseline of 8.2b

bsearch3.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.3s	9315×	body	80	valid
681.0ms	3161×	body	80	nan