Details

sample95.0ms

Algorithm

intervals

Results

37.0ms	302×	body	80	valid
9.0ms	68×	body	80	nan

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	2638
4	446
3	177
2	81
1	36
0	17

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize37.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
5.7b	(/ (* M D) (* 2.0 d))
11.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite112.0ms

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×	`*-un-lft-identity` `add-cube-cbrt`
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` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-/l`

Counts

4 → 113

Calls

4 calls:

29.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
8.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
19.0ms	(/ (* M D) (* 2.0 d))
49.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

651.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
536.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
52.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	3068
1	619
0	236

prune997.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.3b

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))
10.1b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
10.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(/ (* M D) (* 2.0 d))
31.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

series1.7s

Counts

4 → 12

Calls

4 calls:

609.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l)))))
35.0ms	(/ (* M D) (* 2.0 d))
51.0ms	(/ (* M D) (* 2.0 d))
1.0s	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ h l))

simplify2.2s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	2933
1	583
0	211

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize85.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))))
5.7b	(/ (* M D) (* 2.0 d))
5.7b	(/ (* M D) (* 2.0 d))
7.1b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

404×	`add-exp-log`
218×	`prod-exp`
140×	`div-exp`
52×	`add-cbrt-cube`
50×	`pow-exp`
28×	`1-exp`
24×	`cbrt-unprod`
22×	`associate-r`
20×	`times-frac`
19×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-undiv`
10×	`pow-to-exp`
9×	`cbrt-prod`
7×	`pow1`
4×	`add-log-exp`
3×	`associate-*r/` `sqrt-prod` `div-inv`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 172

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))))
11.0ms	(/ (* M D) (* 2.0 d))
10.0ms	(/ (* M D) (* 2.0 d))
117.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))

series1.9s

Counts

4 → 12

Calls

4 calls:

674.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))))
52.0ms	(/ (* M D) (* 2.0 d))
52.0ms	(/ (* M D) (* 2.0 d))
1.2s	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))

simplify1.5s

Counts

184 → 184

Iterations

Iter	Nodes
done	5001
1	1138
0	330

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

localize82.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (- 1.0 (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))))
5.7b	(/ (* M D) (* 2.0 d))
5.8b	(/ (* 2.0 d) (* M D))
7.1b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

404×	`add-exp-log`
218×	`prod-exp`
140×	`div-exp`
52×	`add-cbrt-cube`
50×	`pow-exp`
28×	`1-exp`
24×	`cbrt-unprod`
22×	`associate-r`
20×	`times-frac`
19×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`cbrt-undiv`
10×	`pow-to-exp`
9×	`cbrt-prod`
7×	`pow1`
4×	`add-log-exp`
3×	`associate-*r/` `sqrt-prod` `div-inv`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `pow-prod-down` `associate-l/` `-commutative` `flip--`

Counts

4 → 172

Calls

4 calls:

4.0ms	(sqrt (- 1.0 (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))))
17.0ms	(/ (* M D) (* 2.0 d))
16.0ms	(/ (* 2.0 d) (* M D))
104.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))

series1.7s

Counts

4 → 12

Calls

4 calls:

519.0ms	(sqrt (- 1.0 (* (pow (/ 1 (/ (* 2.0 d) (* M D))) (/ 2.0 2)) (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))))
43.0ms	(/ (* M D) (* 2.0 d))
52.0ms	(/ (* 2.0 d) (* M D))
1.1s	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))

simplify1.5s

Counts

184 → 184

Iterations

Iter	Nodes
done	5000
1	1216
0	353

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.8b

regimes2.4s

Accuracy

19.6% (1.4b remaining)

Error of 9.5b against oracle of 8.1b and baseline of 9.8b

bsearch154.0ms

Steps

Iters	Range		Point
0	-3.2552887468857e-311	-8.1311866652206e-312	-2.0342037067041e-311
10	-inf.0	-5.499013127196744e+290	-1.772133656628061e+308

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	9319×	body	80	valid
437.0ms	3144×	body	80	nan