Details

sample135.0ms

Algorithm

intervals

Results

82.0ms	299×	body	80	valid
17.0ms	76×	body	80	nan

simplify204.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

204.0ms

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

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize31.0ms

Local error

Found 4 expressions with local error:

9.3b	(* (/ h l) (/ (* M D) (* 2 d)))
5.7b	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
5.3b	(/ (* M D) (* 2 d))
5.3b	(/ (* M D) (* 2 d))

rewrite79.0ms

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

40.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
13.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
11.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

190.0ms	(sqrt (- 1 (* (* (/ h l) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))))
83.0ms	(* (/ h l) (/ (* M D) (* 2 d)))
39.0ms	(/ (* M D) (* 2 d))
39.0ms	(/ (* M D) (* 2 d))

simplify25.9s

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))))
1.3s	(* (/ (* (* 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 D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize35.0ms

Local error

Found 4 expressions with local error:

5.7b	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
5.3b	(/ (* M D) (* 2 d))
5.3b	(/ (* M D) (* 2 d))
4.4b	(/ (* h (/ (* M D) (* 2 d))) l)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

Slowest

22.0ms	(/ (* h (/ (* M D) (* 2 d))) l)
20.0ms	(/ (* M D) (* 2 d))
11.0ms	(/ (* M D) (* 2 d))
10.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))

series593.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

398.0ms	(sqrt (- 1 (* (/ (* h (/ (* M D) (* 2 d))) l) (/ (* M D) (* 2 d)))))
119.0ms	(/ (* h (/ (* M D) (* 2 d))) l)
40.0ms	(/ (* M D) (* 2 d))
36.0ms	(/ (* M D) (* 2 d))

simplify19.9s

Counts

60 → 111

Calls

60 calls:

Slowest

1.7s	(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
1.6s	(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.6s	(/ (* (* (* h h) h) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* l l) l))
1.4s	(/ (* (* (* h h) h) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* l l) l))
920.0ms	(/ (* (* (* h (/ (* M D) (* 2 d))) (* h (/ (* M D) (* 2 d)))) (* h (/ (* M D) (* 2 d)))) (* (* l l) l))

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.8b

localize52.0ms

Local error

Found 4 expressions with local error:

19.4b	(cbrt (/ (* M D) (* 2 d)))
19.4b	(cbrt (/ (* M D) (* 2 d)))
19.4b	(cbrt (/ (* M D) (* 2 d)))
5.7b	(sqrt (- 1 (* (/ (* h (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d))))) l) (/ (* M D) (* 2 d)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `times-frac` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 69

Calls

4 calls:

Slowest

20.0ms	(sqrt (- 1 (* (/ (* h (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d))))) l) (/ (* M D) (* 2 d)))))
5.0ms	(cbrt (/ (* M D) (* 2 d)))
5.0ms	(cbrt (/ (* M D) (* 2 d)))
5.0ms	(cbrt (/ (* M D) (* 2 d)))

series971.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

522.0ms	(sqrt (- 1 (* (/ (* h (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d))))) l) (/ (* M D) (* 2 d)))))
161.0ms	(cbrt (/ (* M D) (* 2 d)))
145.0ms	(cbrt (/ (* M D) (* 2 d)))
144.0ms	(cbrt (/ (* M D) (* 2 d)))

simplify4.8s

Counts

37 → 81

Calls

37 calls:

Slowest

590.0ms	(sqrt (- (* 1 1) (* (* (/ (* h (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d))))) l) (/ (* M D) (* 2 d))) (* (/ (* h (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d))))) l) (/ (* M D) (* 2 d))))))
579.0ms	(sqrt (- (pow 1 3) (pow (* (/ (* h (* (* (cbrt (/ (* M D) (* 2 d))) (cbrt (/ (* M D) (* 2 d)))) (cbrt (/ (* M D) (* 2 d))))) l) (/ (* M D) (* 2 d))) 3)))
393.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
318.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
271.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize150.0ms

Local error

Found 4 expressions with local error:

19.4b	(cbrt (/ (* M D) (* 2 d)))
19.4b	(cbrt (/ (* M D) (* 2 d)))
19.4b	(cbrt (/ (* M D) (* 2 d)))
19.4b	(cbrt (/ (* M D) (* 2 d)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `cbrt-div` `times-frac` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

Slowest

16.0ms	(cbrt (/ (* M D) (* 2 d)))
9.0ms	(cbrt (/ (* M D) (* 2 d)))
9.0ms	(cbrt (/ (* M D) (* 2 d)))
4.0ms	(cbrt (/ (* M D) (* 2 d)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(cbrt (/ (* M D) (* 2 d)))
147.0ms	(cbrt (/ (* M D) (* 2 d)))
145.0ms	(cbrt (/ (* M D) (* 2 d)))
140.0ms	(cbrt (/ (* M D) (* 2 d)))

simplify4.2s

Counts

36 → 80

Calls

36 calls:

Slowest

420.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
371.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
364.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
339.0ms	(* (exp (* 1/3 (- (log (/ -1 d)) (+ (log (/ -1 M)) (log (/ -1 D)))))) (cbrt -1/2))
274.0ms	(* (cbrt 1/2) (exp (* 1/3 (- (+ (log M) (log D)) (log d)))))

prune2.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

regimes1.7s

Accuracy

0% (0.6b remaining)

Error of 8.4b against oracle of 7.8b and baseline of 8.4b

bsearch9.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.9s	9315×	body	80	valid
644.0ms	3120×	body	80	nan