Details

sample83.0ms

Algorithm

intervals

Results

45.0ms	314×	body	80	valid
13.0ms	90×	body	80	nan

simplify160.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

160.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize54.0ms

Local error

Found 4 expressions with local error:

11.1b	(* (/ h l) (/ (* M D) (* 2 d)))
4.9b	(/ (* M D) (* 2 d))
4.9b	(/ (* M D) (* 2 d))
4.7b	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

rewrite66.0ms

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

24.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
15.0ms	(/ (* M D) (* 2 d))
11.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
11.0ms	(/ (* M D) (* 2 d))

series393.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

213.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
98.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
43.0ms	(/ (* M D) (* 2 d))
38.0ms	(/ (* M D) (* 2 d))

simplify26.3s

Counts

84 → 133

Calls

84 calls:

Slowest

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

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize30.0ms

Local error

Found 4 expressions with local error:

5.7b	(* h (/ (* M D) (* 2 d)))
4.9b	(/ (* M D) (* 2 d))
4.9b	(/ (* M D) (* 2 d))
4.7b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

rewrite75.0ms

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

38.0ms	(* h (/ (* M D) (* 2 d)))
12.0ms	(/ (* M D) (* 2 d))
11.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
11.0ms	(/ (* M D) (* 2 d))

series551.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

386.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
68.0ms	(* h (/ (* M D) (* 2 d)))
49.0ms	(/ (* M D) (* 2 d))
48.0ms	(/ (* M D) (* 2 d))

simplify17.2s

Counts

60 → 110

Calls

60 calls:

Slowest

1.3s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
1.1s	(* (* (* 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))))
833.0ms	(/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))
779.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize58.0ms

Local error

Found 4 expressions with local error:

5.7b	(* h (/ (* M D) (* 2 d)))
5.7b	(* h (/ (* M D) (* 2 d)))
4.9b	(/ (* M D) (* 2 d))
4.9b	(/ (* M D) (* 2 d))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

Slowest

30.0ms	(* h (/ (* M D) (* 2 d)))
24.0ms	(* h (/ (* M D) (* 2 d)))
22.0ms	(/ (* M D) (* 2 d))
12.0ms	(/ (* M D) (* 2 d))

series214.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

82.0ms	(* h (/ (* M D) (* 2 d)))
61.0ms	(* h (/ (* M D) (* 2 d)))
37.0ms	(/ (* M D) (* 2 d))
34.0ms	(/ (* M D) (* 2 d))

simplify23.6s

Counts

74 → 124

Calls

74 calls:

Slowest

1.5s	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.2s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))
1.2s	(* (* (* 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))))
1.0s	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize99.0ms

Local error

Found 4 expressions with local error:

18.4b	(cbrt (* h (/ (* M D) (* 2 d))))
18.4b	(cbrt (* h (/ (* M D) (* 2 d))))
18.4b	(cbrt (* h (/ (* M D) (* 2 d))))
5.7b	(* h (/ (* M D) (* 2 d)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

Slowest

20.0ms	(cbrt (* h (/ (* M D) (* 2 d))))
20.0ms	(* h (/ (* M D) (* 2 d)))
15.0ms	(cbrt (* h (/ (* M D) (* 2 d))))
13.0ms	(cbrt (* h (/ (* M D) (* 2 d))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

196.0ms	(cbrt (* h (/ (* M D) (* 2 d))))
172.0ms	(cbrt (* h (/ (* M D) (* 2 d))))
170.0ms	(cbrt (* h (/ (* M D) (* 2 d))))
66.0ms	(* h (/ (* M D) (* 2 d)))

simplify11.3s

Counts

39 → 83

Calls

39 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))))
913.0ms	(* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))))
858.0ms	(* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))))
857.0ms	(* 1/2 (/ (* M (* D h)) d))

prune2.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 8.5b

regimes1.5s

Accuracy

0% (0.5b remaining)

Error of 7.9b against oracle of 7.4b and baseline of 7.9b

bsearch20.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.8s	9328×	body	80	valid
585.0ms	3043×	body	80	nan