Details

sample591.0ms

Algorithm

intervals

Results

364.0ms	1169×	body	80	nan
144.0ms	417×	body	80	valid

simplify170.0ms

Calls

1 calls:

Slowest

169.0ms

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize63.0ms

Local error

Found 4 expressions with local error:

12.7b	(pow (/ d h) (/ 1 2))
10.3b	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
10.0b	(pow (/ d l) (/ 1 2))
6.0b	(/ (* M D) (* 2 d))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`add-cube-cbrt`
9×	`prod-exp`
9×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`unpow-prod-down`
8×	`pow-unpow`
8×	`pow1`
6×	`div-inv`
4×	`add-log-exp`
4×	`pow-exp`
4×	`associate-r`
3×	`cbrt-unprod`
3×	`associate-*l/`
3×	`pow-to-exp`
2×	`div-exp`
2×	`pow-pow`
1×	`associate-/l*`
1×	`*-commutative`
1×	`associate-*r/`
1×	`pow-prod-down`
1×	`associate-l`
1×	`times-frac`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`
1×	`cbrt-undiv`
1×	`frac-times`

Calls

4 calls:

Slowest

10.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
2.0ms	(/ (* M D) (* 2 d))
1.0ms	(pow (/ d h) (/ 1 2))
1.0ms	(pow (/ d l) (/ 1 2))

series273.0ms

Calls

4 calls:

Slowest

99.0ms	(pow (/ d l) (/ 1 2))
78.0ms	(pow (/ d h) (/ 1 2))
71.0ms	(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))
25.0ms	(/ (* M D) (* 2 d))

simplify3.7s

Calls

52 calls:

Slowest

685.0ms	(* (* 1 (pow (/ (* M D) (* 2 d)) 2)) h)
460.0ms	(+ (+ (log (/ 1 2)) (log (pow (/ (* M D) (* 2 d)) 2))) (log (/ h l)))
302.0ms	(* (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2))) (* (* (/ h l) (/ h l)) (/ h l)))
165.0ms	(exp (* 1/2 (- (log (/ 1 h)) (log (/ 1 d)))))
159.0ms	(exp (* 1/2 (- (log (/ 1 l)) (log (/ 1 d)))))

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.5b

localize18.0ms

Local error

Found 4 expressions with local error:

12.7b	(pow (/ d h) (/ 1 2))
10.3b	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
10.0b	(pow (/ d l) (/ 1 2))
5.9b	(/ (* 2 d) (* M D))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
11×	`prod-exp`
11×	`add-cbrt-cube`
9×	`add-cube-cbrt`
9×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`unpow-prod-down`
8×	`pow-unpow`
8×	`pow1`
6×	`div-inv`
5×	`pow-exp`
4×	`add-log-exp`
4×	`associate-r`
3×	`cbrt-unprod`
3×	`associate-*l/`
3×	`pow-to-exp`
2×	`div-exp`
2×	`pow-pow`
2×	`rec-exp`
1×	`associate-/l*`
1×	`*-commutative`
1×	`associate-*r/`
1×	`pow-prod-down`
1×	`associate-l`
1×	`times-frac`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`
1×	`cbrt-undiv`
1×	`frac-times`

Calls

4 calls:

Slowest

19.0ms	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
5.0ms	(/ (* 2 d) (* M D))
3.0ms	(pow (/ d l) (/ 1 2))
1.0ms	(pow (/ d h) (/ 1 2))

series286.0ms

Calls

4 calls:

Slowest

100.0ms	(pow (/ d l) (/ 1 2))
86.0ms	(pow (/ d h) (/ 1 2))
71.0ms	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
29.0ms	(/ (* 2 d) (* M D))

simplify6.6s

Calls

53 calls:

Slowest

1.2s	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
1.1s	(+ (log (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2))) (log (/ h l)))
769.0ms	(* (* 1 (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
608.0ms	(+ (+ (log (/ 1 2)) (log (pow (/ 1 (/ (* 2 d) (* M D))) 2))) (log (/ h l)))
531.0ms	(* (* 1 (pow (/ 1 (/ (* 2 d) (* M D))) 2)) h)

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.5b

localize29.0ms

Local error

Found 4 expressions with local error:

12.7b	(pow (/ d h) (/ 1 2))
10.3b	(* (* (/ 1 2) (pow (/ M (/ (* 2 d) D)) 2)) (/ h l))
10.0b	(pow (/ d l) (/ 1 2))
6.3b	(/ M (/ (* 2 d) D))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
10×	`add-cube-cbrt`
10×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cbrt-cube`
8×	`unpow-prod-down`
8×	`pow-unpow`
8×	`pow1`
7×	`div-inv`
7×	`prod-exp`
4×	`add-log-exp`
4×	`associate-r`
4×	`associate-/r*`
3×	`cbrt-unprod`
3×	`pow-exp`
3×	`associate-*l/`
3×	`pow-to-exp`
2×	`pow-pow`
1×	`*-commutative`
1×	`associate-/r/`
1×	`associate-*r/`
1×	`pow-prod-down`
1×	`associate-l`
1×	`frac-2neg`
1×	`clear-num`
1×	`frac-times`

Calls

4 calls:

Slowest

19.0ms	(* (* (/ 1 2) (pow (/ M (/ (* 2 d) D)) 2)) (/ h l))
2.0ms	(pow (/ d h) (/ 1 2))
2.0ms	(pow (/ d l) (/ 1 2))
1.0ms	(/ M (/ (* 2 d) D))

series187.0ms

Calls

4 calls:

Slowest

62.0ms	(pow (/ d h) (/ 1 2))
57.0ms	(pow (/ d l) (/ 1 2))
51.0ms	(* (* (/ 1 2) (pow (/ M (/ (* 2 d) D)) 2)) (/ h l))
17.0ms	(/ M (/ (* 2 d) D))

simplify3.6s

Calls

51 calls:

Slowest

618.0ms	(* (* (/ 1 2) (pow (/ M (/ (* 2 d) D)) 2)) (/ h l))
408.0ms	(+ (log (* (/ 1 2) (pow (/ M (/ (* 2 d) D)) 2))) (log (/ h l)))
307.0ms	(* (* 1 (pow (/ M (/ (* 2 d) D)) 2)) (/ h l))
271.0ms	(+ (+ (log (/ 1 2)) (* (log (/ M (/ (* 2 d) D))) 2)) (log (/ h l)))
248.0ms	(+ (+ (log (/ 1 2)) (* (log (/ M (/ (* 2 d) D))) 2)) (log (/ h l)))

prune1.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize18.0ms

Local error

Found 4 expressions with local error:

12.7b	(pow (/ d h) (/ 1 2))
12.7b	(pow (/ d h) (/ 1 2))
10.3b	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
10.0b	(pow (/ d l) (/ 1 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
12×	`unpow-prod-down`
12×	`pow-unpow`
11×	`add-cube-cbrt`
11×	`prod-exp`
11×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
9×	`add-cbrt-cube`
9×	`pow1`
7×	`div-inv`
6×	`pow-exp`
4×	`add-log-exp`
4×	`associate-r`
4×	`pow-to-exp`
3×	`cbrt-unprod`
3×	`associate-*l/`
3×	`pow-pow`
2×	`rec-exp`
1×	`*-commutative`
1×	`associate-*r/`
1×	`pow-prod-down`
1×	`associate-l`
1×	`div-exp`
1×	`frac-times`

Calls

4 calls:

Slowest

19.0ms	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
3.0ms	(pow (/ d h) (/ 1 2))
3.0ms	(pow (/ d h) (/ 1 2))
2.0ms	(pow (/ d l) (/ 1 2))

series271.0ms

Calls

4 calls:

Slowest

74.0ms	(pow (/ d l) (/ 1 2))
74.0ms	(pow (/ d h) (/ 1 2))
63.0ms	(pow (/ d h) (/ 1 2))
60.0ms	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))

simplify6.6s

Calls

59 calls:

Slowest

1.1s	(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
805.0ms	(* (* 1 (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
788.0ms	(+ (log (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2))) (log (/ h l)))
660.0ms	(+ (+ (log (/ 1 2)) (log (pow (/ 1 (/ (* 2 d) (* M D))) 2))) (log (/ h l)))
576.0ms	(* (* 1 (pow (/ 1 (/ (* 2 d) (* M D))) 2)) h)

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.2b

regimes1.4s

Accuracy

48.1% (7.1b remaining)

Error of 19.7b against oracle of 12.6b and baseline of 26.3b

bsearch1.7s

end0.0ms

sample23.3s

Algorithm

intervals

Results

15.1s	37877×	body	80	nan
5.8s	12887×	body	80	valid