Details

sample60.0ms

Algorithm

intervals

Results

22.0ms	301×	body	80	valid
8.0ms	106×	body	80	nan

simplify4.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	4261
5	1442
4	379
3	165
2	79
1	36
0	17

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize33.0ms

Local error

Found 4 expressions with local error:

2.9b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.8b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
4.8b	(/ (* M D) (* 2.0 d))
10.5b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite125.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `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 → 121

Calls

4 calls:

30.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
12.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
27.0ms	(/ (* M D) (* 2.0 d))
51.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.3s

Counts

4 → 12

Calls

4 calls:

586.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
617.0ms	(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))

simplify1.9s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2337
1	624
0	244

prune916.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.1b

localize79.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))
2.9b	(* w0 (sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l))))))
3.8b	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))))
5.3b	(/ M (/ (* 2.0 d) D))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
120×	`times-frac`
64×	`*-un-lft-identity` `add-cube-cbrt`
55×	`add-exp-log`
52×	`cbrt-prod`
43×	`associate-l`
36×	`unpow-prod-down` `associate-r`
22×	`unswap-sqr`
21×	`div-exp`
18×	`add-cbrt-cube`
16×	`prod-exp`
10×	`div-inv`
8×	`pow-exp`
7×	`pow1` `associate-/r*` `sqrt-prod`
6×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `sqrt-div` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `flip3--` `associate-r/` `associate-/r/` `-commutative` `flip--`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-*l/`

Counts

4 → 208

Calls

4 calls:

58.0ms	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))
16.0ms	(* w0 (sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l))))))
11.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))))
8.0ms	(/ M (/ (* 2.0 d) D))

series1.4s

Counts

4 → 12

Calls

4 calls:

694.0ms	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))
359.0ms	(* w0 (sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l))))))
264.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))))
46.0ms	(/ M (/ (* 2.0 d) D))

simplify2.8s

Counts

220 → 220

Iterations

Iter	Nodes
done	5022
2	3665
1	1086
0	393

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize108.0ms

Local error

Found 4 expressions with local error:

3.7b	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)))
3.8b	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))
5.3b	(/ M (/ (* 2.0 d) D))
5.3b	(/ M (/ (* 2.0 d) D))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
134×	`add-sqr-sqrt`
77×	`*-un-lft-identity` `add-cube-cbrt`
62×	`add-exp-log`
52×	`cbrt-prod`
40×	`associate-l`
36×	`unpow-prod-down`
30×	`associate-r`
26×	`div-exp`
25×	`add-cbrt-cube`
20×	`unswap-sqr`
16×	`prod-exp`
15×	`div-inv`
14×	`associate-/r*`
11×	`cbrt-undiv`
8×	`pow-exp`
6×	`associate-/l*` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/` `sqrt-prod`
2×	`pow-to-exp` `clear-num` `frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l/` `-commutative` `flip--`

Counts

4 → 232

Calls

4 calls:

116.0ms	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)))
11.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))
16.0ms	(/ M (/ (* 2.0 d) D))
8.0ms	(/ M (/ (* 2.0 d) D))

series1.2s

Counts

4 → 12

Calls

4 calls:

763.0ms	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)))
304.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2)))) (/ (cbrt h) (cbrt l)))))
58.0ms	(/ M (/ (* 2.0 d) D))
54.0ms	(/ M (/ (* 2.0 d) D))

simplify2.5s

Counts

244 → 244

Iterations

Iter	Nodes
done	5004
2	3236
1	941
0	367

prune3.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.2b

localize192.0ms

Local error

Found 4 expressions with local error:

5.3b	(/ M (/ (* 2.0 d) D))
17.3b	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))
17.3b	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))
17.3b	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-l/` `associate-/l`
1×	`clear-num` `frac-2neg` `prod-exp` `associate-/r/` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

13.0ms	(/ M (/ (* 2.0 d) D))
15.0ms	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))
15.0ms	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))
23.0ms	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))

series2.4s

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ M (/ (* 2.0 d) D))
774.0ms	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))
791.0ms	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))
750.0ms	(cbrt (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) (/ 2.0 2))))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1542
1	432
0	185

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

regimes2.2s

Accuracy

2.3% (1.6b remaining)

Error of 9.1b against oracle of 7.4b and baseline of 9.1b

bsearch278.0ms

Steps

Iters	Range		Point
9	1.3998448074383232e+208	6.303241018661559e+213	6.489671467557263e+210
7	2.213004195561125e+122	1.180743632160318e+124	3.5822571380375866e+122

simplify19.0ms

Iterations

Iter	Nodes
done	62
1	62
0	46

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	9267×	body	80	valid
412.0ms	3027×	body	80	nan