Details

sample77.0ms

Algorithm

intervals

Results

31.0ms	288×	body	80	valid
11.0ms	97×	body	80	nan

simplify5.1s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize55.0ms

Local error

Found 4 expressions with local error:

0.5b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.0b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.5b	(/ (* M D) (* 2.0 d))
12.0b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite99.0ms

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:

28.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
11.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
21.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.2s

Counts

4 → 12

Calls

4 calls:

626.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
559.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
36.0ms	(/ (* M D) (* 2.0 d))
963.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify2.0s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2337
1	624
0	244

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize92.0ms

Local error

Found 4 expressions with local error:

2.6b	(* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))
3.1b	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))
3.5b	(/ M (/ (* 2.0 d) D))
4.0b	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))))

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

378×	`add-exp-log`
177×	`prod-exp`
156×	`times-frac`
143×	`add-sqr-sqrt`
138×	`div-exp`
88×	`cbrt-prod`
86×	`*-un-lft-identity` `add-cube-cbrt`
70×	`associate-r`
47×	`add-cbrt-cube`
41×	`associate-l`
40×	`pow-exp`
37×	`cbrt-unprod`
36×	`unpow-prod-down`
23×	`cbrt-undiv`
20×	`unswap-sqr`
11×	`div-inv`
10×	`pow-to-exp` `pow1` `associate-*l/`
7×	`associate-/r*`
6×	`sqr-pow`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-r/` `sqrt-prod` `associate-/l`
2×	`sqrt-div` `associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 310

Calls

4 calls:

310.0ms	(* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))
86.0ms	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))
17.0ms	(/ M (/ (* 2.0 d) D))
13.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

1.4s	(* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))
786.0ms	(* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))
53.0ms	(/ M (/ (* 2.0 d) D))
283.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (/ (cbrt h) (cbrt l)) (pow (/ M (/ (* 2.0 d) D)) 2.0))) (/ (cbrt h) (cbrt l)))))

simplify2.4s

Counts

322 → 322

Iterations

Iter	Nodes
done	5000
1	1649
0	558

prune3.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize179.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ (* (cbrt M) (cbrt M)) (* (cbrt (/ (* 2.0 d) D)) (cbrt (/ (* 2.0 d) D)))) 2.0)) (pow (/ (cbrt M) (cbrt (/ (* 2.0 d) D))) 2.0))) (/ (cbrt h) (cbrt l)))))
11.0b	(cbrt (/ (* 2.0 d) D))
11.0b	(cbrt (/ (* 2.0 d) D))
11.0b	(cbrt (/ (* 2.0 d) D))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ (* (cbrt M) (cbrt M)) (* (cbrt (/ (* 2.0 d) D)) (cbrt (/ (* 2.0 d) D)))) 2.0)) (pow (/ (cbrt M) (cbrt (/ (* 2.0 d) D))) 2.0))) (/ (cbrt h) (cbrt l)))))
5.0ms	(cbrt (/ (* 2.0 d) D))
5.0ms	(cbrt (/ (* 2.0 d) D))
6.0ms	(cbrt (/ (* 2.0 d) D))

series1.2s

Counts

4 → 12

Calls

4 calls:

730.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ (* (cbrt M) (cbrt M)) (* (cbrt (/ (* 2.0 d) D)) (cbrt (/ (* 2.0 d) D)))) 2.0)) (pow (/ (cbrt M) (cbrt (/ (* 2.0 d) D))) 2.0))) (/ (cbrt h) (cbrt l)))))
143.0ms	(cbrt (/ (* 2.0 d) D))
153.0ms	(cbrt (/ (* 2.0 d) D))
139.0ms	(cbrt (/ (* 2.0 d) D))

simplify4.3s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	2924
2	573
1	216
0	114

prune1.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize230.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ (* (cbrt M) (cbrt M)) (* (cbrt (/ (* 2.0 d) D)) (cbrt (/ (* 2.0 d) D)))) 2.0)) (pow (/ (cbrt M) (* (cbrt (/ 2.0 (* (cbrt D) (cbrt D)))) (cbrt (/ d (cbrt D))))) 2.0))) (/ (cbrt h) (cbrt l)))))
4.4b	(cbrt (/ d (cbrt D)))
11.0b	(cbrt (/ (* 2.0 d) D))
11.0b	(cbrt (/ (* 2.0 d) D))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

45×	`cbrt-prod`
24×	`times-frac`
23×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `sqrt-prod` `div-inv`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 86

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ (* (cbrt M) (cbrt M)) (* (cbrt (/ (* 2.0 d) D)) (cbrt (/ (* 2.0 d) D)))) 2.0)) (pow (/ (cbrt M) (* (cbrt (/ 2.0 (* (cbrt D) (cbrt D)))) (cbrt (/ d (cbrt D))))) 2.0))) (/ (cbrt h) (cbrt l)))))
3.0ms	(cbrt (/ d (cbrt D)))
3.0ms	(cbrt (/ (* 2.0 d) D))
7.0ms	(cbrt (/ (* 2.0 d) D))

series1.2s

Counts

4 → 12

Calls

4 calls:

728.0ms	(sqrt (- 1.0 (* (* (/ (cbrt h) (cbrt l)) (* (* (/ (cbrt h) (cbrt l)) (pow (/ (* (cbrt M) (cbrt M)) (* (cbrt (/ (* 2.0 d) D)) (cbrt (/ (* 2.0 d) D)))) 2.0)) (pow (/ (cbrt M) (* (cbrt (/ 2.0 (* (cbrt D) (cbrt D)))) (cbrt (/ d (cbrt D))))) 2.0))) (/ (cbrt h) (cbrt l)))))
281.0ms	(cbrt (/ d (cbrt D)))
122.0ms	(cbrt (/ (* 2.0 d) D))
105.0ms	(cbrt (/ (* 2.0 d) D))

simplify5.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5003
3	3677
2	840
1	352
0	203

prune1.5s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.0b

regimes4.0s

Accuracy

0% (1.6b remaining)

Error of 8.9b against oracle of 7.3b and baseline of 8.9b

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	9297×	body	80	valid
412.0ms	3005×	body	80	nan