Details

sample73.0ms

Algorithm

intervals

Results

27.0ms	300×	body	80	valid
8.0ms	92×	body	80	nan

simplify51.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize43.0ms

Local error

Found 4 expressions with local error:

2.2b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.5b	(/ (* M D) (* 2.0 d))
11.1b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
35×	`add-sqr-sqrt`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp` `associate-r`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`times-frac`
12×	`associate-l`
10×	`pow-exp`
8×	`unswap-sqr`
7×	`pow1` `unpow-prod-down` `sqrt-prod` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-*r/` `div-inv` `sqr-pow`
2×	`pow-to-exp` `flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 113

Calls

4 calls:

27.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
6.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
26.0ms	(/ (* M D) (* 2.0 d))
42.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.6s

Counts

4 → 12

Calls

4 calls:

570.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
997.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
38.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify68.0ms

Counts: 125 → 125

prune680.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.5b

localize49.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
4.2b	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
5.5b	(/ (* M D) (* 2.0 d))
7.8b	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

210×	`add-exp-log`
85×	`div-exp`
79×	`prod-exp`
57×	`times-frac`
55×	`add-sqr-sqrt`
33×	`add-cbrt-cube`
30×	`pow-exp`
25×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r`
18×	`unpow-prod-down`
13×	`cbrt-undiv` `cbrt-prod` `associate-l` `cbrt-unprod`
12×	`unswap-sqr`
10×	`associate-/l*`
7×	`pow1` `div-inv`
6×	`pow-to-exp` `sqr-pow`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r*`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 176

Calls

4 calls:

27.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
5.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
22.0ms	(/ (* M D) (* 2.0 d))
106.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

series2.4s

Counts

4 → 12

Calls

4 calls:

668.0ms	(/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l)))
665.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
30.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (/ (pow (/ (* M D) (* 2.0 d)) 2.0) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))

simplify119.0ms

Counts: 188 → 188

prune928.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.2b

localize70.0ms

Local error

Found 4 expressions with local error:

4.2b	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
5.5b	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

118×	`add-sqr-sqrt`
112×	`times-frac`
96×	`add-exp-log`
58×	`associate-l`
52×	`cbrt-prod`
49×	`add-cube-cbrt` `*-un-lft-identity`
38×	`div-exp`
36×	`unpow-prod-down` `add-cbrt-cube`
32×	`prod-exp`
22×	`associate-r`
21×	`unswap-sqr`
12×	`cbrt-undiv` `cbrt-unprod` `sqr-pow`
10×	`pow-exp` `div-inv`
7×	`pow1`
4×	`add-log-exp`
3×	`sqrt-prod`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 190

Calls

4 calls:

10.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
113.0ms	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))
25.0ms	(/ (* M D) (* 2.0 d))
27.0ms	(/ (* M D) (* 2.0 d))

series2.0s

Counts

4 → 12

Calls

4 calls:

620.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l))))))
1.2s	(* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (/ h (cbrt l)))
52.0ms	(/ (* M D) (* 2.0 d))
61.0ms	(/ (* M D) (* 2.0 d))

simplify126.0ms

Counts: 202 → 202

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

localize70.0ms

Local error

Found 4 expressions with local error:

3.5b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h)))
4.2b	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt l)) (/ (cbrt h) (cbrt l))))))
5.5b	(/ (* M D) (* 2.0 d))
5.5b	(/ (* M D) (* 2.0 d))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
37×	`prod-exp`
31×	`add-cbrt-cube`
16×	`div-exp`
11×	`cbrt-unprod`
10×	`add-sqr-sqrt` `pow-exp`
9×	`associate-l`
8×	`cbrt-undiv`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1`
4×	`add-log-exp`
3×	`times-frac` `sqrt-prod` `div-inv` `unswap-sqr`
2×	`pow-to-exp` `frac-2neg` `sqrt-div` `clear-num` `associate-/r` `associate-/l` `sqr-pow`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `flip--`

Counts

4 → 94

Calls

4 calls:

57.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h)))
7.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt l)) (/ (cbrt h) (cbrt l))))))
13.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(/ (* M D) (* 2.0 d))

series1.3s

Counts

4 → 12

Calls

4 calls:

652.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h)))
602.0ms	(sqrt (- 1.0 (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (* (/ (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (cbrt h) (cbrt h))) (cbrt l)) (/ (cbrt h) (cbrt l))))))
49.0ms	(/ (* M D) (* 2.0 d))
34.0ms	(/ (* M D) (* 2.0 d))

simplify95.0ms

Counts: 106 → 106

prune676.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.2b

regimes1.3s

Accuracy

-20.3% (1.5b remaining)

Error of 8.5b against oracle of 7.0b and baseline of 8.3b

bsearch104.0ms

Steps

Iters	Range		Point
6	-3.866591879667067e+158	-8.084796982885134e+157	-3.827325132878031e+158

simplify27.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	9297×	body	80	valid
790.0ms	3139×	body	80	nan