Details

sample83.0ms

Algorithm

intervals

Results

49.0ms	293×	body	80	valid
15.0ms	101×	body	80	nan

simplify184.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

184.0ms

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize50.0ms

Local error

Found 4 expressions with local error:

11.0b	(* (/ h l) (/ (* M D) (* 2 d)))
4.8b	(/ (* M D) (* 2 d))
4.8b	(/ (* M D) (* 2 d))
4.4b	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite104.0ms

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

53.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
21.0ms	(/ (* M D) (* 2 d))
20.0ms	(/ (* M D) (* 2 d))
8.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series352.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

188.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
88.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
46.0ms	(/ (* M D) (* 2 d))
30.0ms	(/ (* M D) (* 2 d))

simplify26.1s

Counts

84 → 133

Calls

84 calls:

Slowest

1.7s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) 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))))
1.3s	(* (* (* (/ h l) (/ h l)) (/ h l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.3s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.3s	(* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

localize34.0ms

Local error

Found 4 expressions with local error:

5.0b	(* h (/ (* M D) (* 2 d)))
4.8b	(/ (* M D) (* 2 d))
4.8b	(/ (* M D) (* 2 d))
4.4b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

rewrite57.0ms

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

25.0ms	(* h (/ (* M D) (* 2 d)))
15.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
5.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series557.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

406.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
77.0ms	(* h (/ (* M D) (* 2 d)))
37.0ms	(/ (* M D) (* 2 d))
36.0ms	(/ (* M D) (* 2 d))

simplify17.3s

Counts

60 → 110

Calls

60 calls:

Slowest

1.1s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.0s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
941.0ms	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
792.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
787.0ms	(+ (log h) (- (log (* M D)) (+ (log 2) (log d))))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize50.0ms

Local error

Found 4 expressions with local error:

5.0b	(* h (* (* M D) (/ 1 (* 2 d))))
4.9b	(* (* M D) (/ 1 (* 2 d)))
4.8b	(/ (* M D) (* 2 d))
4.4b	(sqrt (- 1 (* (/ (* h (* (* M D) (/ 1 (* 2 d)))) l) (/ (* M D) (* 2 d)))))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
73×	`prod-exp`
66×	`add-cbrt-cube`
33×	`cbrt-unprod`
20×	`div-exp`
19×	`pow1`
12×	`cbrt-undiv`
9×	`add-sqr-sqrt` `pow-prod-down`
8×	`rec-exp` `-un-lft-identity` `1-exp` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `times-frac` `associate-l` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`sqrt-div` `un-div-inv` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--` `associate-/l`

Counts

4 → 127

Calls

4 calls:

Slowest

94.0ms	(* h (* (* M D) (/ 1 (* 2 d))))
53.0ms	(* (* M D) (/ 1 (* 2 d)))
11.0ms	(/ (* M D) (* 2 d))
5.0ms	(sqrt (- 1 (* (/ (* h (* (* M D) (/ 1 (* 2 d)))) l) (/ (* M D) (* 2 d)))))

series547.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

386.0ms	(sqrt (- 1 (* (/ (* h (* (* M D) (/ 1 (* 2 d)))) l) (/ (* M D) (* 2 d)))))
80.0ms	(* h (* (* M D) (/ 1 (* 2 d))))
41.0ms	(/ (* M D) (* 2 d))
40.0ms	(* (* M D) (/ 1 (* 2 d)))

simplify25.1s

Counts

90 → 139

Calls

90 calls:

Slowest

986.0ms	(* (* (* h h) h) (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* 1 1) 1) (* (* (* 2 d) (* 2 d)) (* 2 d)))))
830.0ms	(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
819.0ms	(sqrt (- (pow 1 3) (pow (* (/ (* h (* (* M D) (/ 1 (* 2 d)))) l) (/ (* M D) (* 2 d))) 3)))
740.0ms	(sqrt (- (* 1 1) (* (* (/ (* h (* (* M D) (/ 1 (* 2 d)))) l) (/ (* M D) (* 2 d))) (* (/ (* h (* (* M D) (/ 1 (* 2 d)))) l) (/ (* M D) (* 2 d))))))
613.0ms	(+ (log (* M D)) (- (log 1) (+ (log 2) (log d))))

prune2.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.8b

localize57.0ms

Local error

Found 4 expressions with local error:

16.4b	(cbrt (/ (* M D) (* 2 d)))
16.4b	(cbrt (/ (* M D) (* 2 d)))
16.4b	(cbrt (/ (* M D) (* 2 d)))
5.0b	(* h (/ (* M D) (* 2 d)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-cbrt-cube` `add-exp-log`
15×	`cbrt-prod`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `cbrt-undiv` `times-frac` `div-exp` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-l`
1×	`pow-prod-down` `associate-r/` `-commutative` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

Slowest

32.0ms	(* h (/ (* M D) (* 2 d)))
7.0ms	(cbrt (/ (* M D) (* 2 d)))
4.0ms	(cbrt (/ (* M D) (* 2 d)))
4.0ms	(cbrt (/ (* M D) (* 2 d)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

161.0ms	(cbrt (/ (* M D) (* 2 d)))
154.0ms	(cbrt (/ (* M D) (* 2 d)))
133.0ms	(cbrt (/ (* M D) (* 2 d)))
66.0ms	(* h (/ (* M D) (* 2 d)))

simplify11.5s

Counts

51 → 95

Calls

51 calls:

Slowest

1.3s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.1s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
864.0ms	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
847.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
529.0ms	(+ (log h) (- (+ (log M) (log D)) (+ (log 2) (log d))))

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

regimes1.3s

Accuracy

0% (0.4b remaining)

Error of 8.0b against oracle of 7.5b and baseline of 8.0b

bsearch4.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.4s	9350×	body	80	valid
589.0ms	3113×	body	80	nan