Details

sample71.0ms

Algorithm

intervals

Results

31.0ms	302×	body	80	valid
7.0ms	104×	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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize36.0ms

Local error

Found 4 expressions with local error:

1.5b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
4.7b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
6.1b	(/ (* M D) (* 2.0 d))
11.3b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite84.0ms

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:

26.0ms	(* 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))))
9.0ms	(/ (* M D) (* 2.0 d))
35.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series2.6s

Counts

4 → 12

Calls

4 calls:

592.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
552.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
36.0ms	(/ (* M D) (* 2.0 d))
1.4s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify1.8s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	2337
1	624
0	244

prune925.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize57.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
4.7b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
6.1b	(/ (* M D) (* 2.0 d))
6.6b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-exp-log`
91×	`prod-exp`
40×	`div-exp`
30×	`add-cbrt-cube`
25×	`pow-exp`
21×	`add-sqr-sqrt`
16×	`associate-r`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`times-frac` `cbrt-unprod`
10×	`associate-l`
8×	`rec-exp` `1-exp`
7×	`pow1`
6×	`cbrt-undiv` `unpow-prod-down`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv` `unswap-sqr`
2×	`sqrt-div` `*-commutative` `sqr-pow`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `flip--` `associate-/l*`

Counts

4 → 136

Calls

4 calls:

42.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
5.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
9.0ms	(/ (* M D) (* 2.0 d))
32.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

series2.7s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))
528.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) 2.0) h) (/ 1 l))))
51.0ms	(/ (* M D) (* 2.0 d))
1.1s	(* (pow (/ (* M D) (* 2.0 d)) 2.0) h)

simplify2.1s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
2	2626
1	722
0	277

prune973.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize43.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
4.7b	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
6.1b	(/ (* M D) (* 2.0 d))
6.1b	(/ (* M D) (* 2.0 d))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

1381×	`add-exp-log`
896×	`prod-exp`
362×	`div-exp`
300×	`pow-exp`
60×	`pow-to-exp`
57×	`rec-exp` `1-exp`
49×	`add-cbrt-cube`
20×	`cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cbrt-undiv` `times-frac`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`clear-num` `associate-/r` `frac-2neg` `sqrt-div` `associate-/l`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-l` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `flip--`

Counts

4 → 324

Calls

4 calls:

115.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
5.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
9.0ms	(/ (* M D) (* 2.0 d))
9.0ms	(/ (* M D) (* 2.0 d))

series1.6s

Counts

4 → 12

Calls

4 calls:

953.0ms	(* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))
532.0ms	(sqrt (- 1.0 (* (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) h)) (/ 1 l))))
36.0ms	(/ (* M D) (* 2.0 d))
56.0ms	(/ (* M D) (* 2.0 d))

simplify2.4s

Counts

336 → 336

Iterations

Iter	Nodes
done	5474
2	2830
1	954
0	424

prune877.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize52.0ms

Local error

Found 4 expressions with local error:

4.2b	(* (* (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))) (/ 1 l))
4.7b	(sqrt (- 1.0 (* (* (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))) (/ 1 l))))
7.6b	(* (/ D d) (/ M 2.0))
7.6b	(* (/ D d) (/ M 2.0))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

1381×	`add-exp-log`
896×	`prod-exp`
362×	`div-exp`
300×	`pow-exp`
65×	`add-sqr-sqrt`
60×	`pow-to-exp`
57×	`rec-exp` `1-exp`
53×	`times-frac`
49×	`add-cbrt-cube`
40×	`*-un-lft-identity` `add-cube-cbrt`
39×	`associate-r`
27×	`associate-l`
20×	`cbrt-unprod`
11×	`pow1` `cbrt-undiv`
8×	`unswap-sqr`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `associate-r/` `-commutative` `sqrt-prod`
2×	`frac-times` `sqrt-div` `associate-*l/`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `un-div-inv` `flip--`

Counts

4 → 382

Calls

4 calls:

80.0ms	(* (* (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))) (/ 1 l))
9.0ms	(sqrt (- 1.0 (* (* (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))) (/ 1 l))))
19.0ms	(* (/ D d) (/ M 2.0))
21.0ms	(* (/ D d) (/ M 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

990.0ms	(* (* (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))) (/ 1 l))
467.0ms	(sqrt (- 1.0 (* (* (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)) (* h (pow (* (/ D d) (/ M 2.0)) (/ 2.0 2)))) (/ 1 l))))
47.0ms	(* (/ D d) (/ M 2.0))
56.0ms	(* (/ D d) (/ M 2.0))

simplify2.7s

Counts

394 → 394

Iterations

Iter	Nodes
done	5000
2	2970
1	1119
0	480

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.3b

regimes2.6s

Accuracy

30.1% (1.6b remaining)

Error of 8.7b against oracle of 7.1b and baseline of 9.4b

bsearch3.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	48
1	48
0	35

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	9265×	body	80	valid
363.0ms	3173×	body	80	nan