Details

sample348.0ms

Algorithm

intervals

Results

134.0ms	72×	body	5120	valid
44.0ms	388×	body	80	nan
39.0ms	58×	body	2560	valid
25.0ms	206×	body	80	valid
21.0ms	38×	body	1280	valid
15.0ms	16×	body	10240	exit
5.0ms	12×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	3344
2	289
1	59
0	21

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.7b

localize76.0ms

Local error

Found 4 expressions with local error:

11.1b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
11.1b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
13.6b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
27.2b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-cbrt-cube` `add-exp-log`
48×	`cbrt-undiv` `div-exp`
42×	`add-sqr-sqrt`
40×	`prod-exp` `cbrt-unprod`
32×	`times-frac` `sqrt-div`
26×	`frac-times` `associate-r`
24×	`frac-add`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l/` `associate-r/`
14×	`associate-l`
13×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`pow1`
8×	`unswap-sqr`
6×	`add-log-exp`
4×	`div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `sum-log` `pow1/2` `sqrt-prod`

Counts

4 → 174

Calls

4 calls:

45.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
42.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
42.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
73.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

series2.0s

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
70.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
803.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
1.1s	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

simplify2.4s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	4720
1	950
0	325

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 48.9b

localize168.0ms

Local error

Found 4 expressions with local error:

13.6b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
27.2b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
27.2b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
27.2b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

80×	`sqrt-div`
72×	`frac-add`
64×	`frac-times`
44×	`associate-l/` `associate-r/`
33×	`flip3-+` `flip-+`
30×	`flip3--` `flip--`
10×	`add-log-exp`
7×	`pow1`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`+-commutative` `sum-log`
2×	`sqrt-pow1`
1×	`pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 124

Calls

4 calls:

39.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
61.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
46.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
55.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

series3.4s

Counts

4 → 12

Calls

4 calls:

805.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
988.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
803.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
812.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

simplify2.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	1832
1	519
0	200

prune2.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 48.9b

localize115.0ms

Local error

Found 4 expressions with local error:

11.1b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
11.1b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
13.6b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M)))
32.7b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

rewrite673.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-cbrt-cube` `add-exp-log`
48×	`cbrt-undiv` `div-exp`
42×	`add-sqr-sqrt`
40×	`prod-exp` `cbrt-unprod`
32×	`times-frac` `sqrt-div`
26×	`frac-times` `associate-r`
24×	`frac-add`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l/` `associate-r/`
14×	`associate-l`
13×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`pow1`
8×	`unswap-sqr`
6×	`add-log-exp`
4×	`div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `sum-log` `pow1/2` `sqrt-prod`

Counts

4 → 174

Calls

4 calls:

45.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
51.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
243.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M)))
324.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

series1.9s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
86.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
774.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M)))
941.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

simplify1.5s

Counts

186 → 186

Iterations

Iter	Nodes
done	5001
1	985
0	328

prune1.7s

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 48.3b

localize99.0ms

Local error

Found 4 expressions with local error:

10.2b	(cbrt (/ c0 w))
11.1b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
13.6b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M)))
37.6b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M))) (* (/ (/ d D) (* (cbrt h) (cbrt h))) (* (/ (/ d D) (cbrt h)) (/ c0 w))))

rewrite777.0ms

Algorithm

rewrite-expression-head

Rules

73×	`frac-times`
64×	`sqrt-div`
60×	`add-cbrt-cube` `add-exp-log`
57×	`associate-*r/`
56×	`frac-add`
41×	`associate-*l/`
30×	`add-sqr-sqrt`
25×	`flip3-+` `times-frac` `flip-+`
24×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
20×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
13×	`cbrt-prod` `associate-r`
9×	`pow1`
7×	`associate-l`
6×	`add-log-exp`
4×	`unswap-sqr`
3×	`div-inv`
2×	`sqrt-pow1` `pow-prod-down`
1×	`+-commutative` `cbrt-div` `sum-log` `pow1/2` `pow1/3` `*-commutative` `sqrt-prod`

Counts

4 → 168

Calls

4 calls:

3.0ms	(cbrt (/ c0 w))
60.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
358.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M)))
337.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M))) (* (/ (/ d D) (* (cbrt h) (cbrt h))) (* (/ (/ d D) (cbrt h)) (/ c0 w))))

series2.1s

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (/ c0 w))
94.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
838.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M)))
1.1s	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (* (/ (* (/ d D) (/ d D)) h) (* (cbrt (/ c0 w)) (cbrt (/ c0 w)))) (cbrt (/ c0 w))) M))) (* (/ (/ d D) (* (cbrt h) (cbrt h))) (* (/ (/ d D) (cbrt h)) (/ c0 w))))

simplify2.3s

Counts

180 → 180

Iterations

Iter	Nodes
done	5001
1	1474
0	526

prune2.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 47.1b

regimes2.3s

Accuracy

-11.5% (8.4b remaining)

Error of 54.7b against oracle of 46.3b and baseline of 53.8b

bsearch482.0ms

Steps

Iters	Range		Point
5	4.846208048690604e+207	1.9185947707515486e+208	4.9256944603241056e+207
9	1.4017454010330405e-86	1.4861608940541164e-78	3.524321437088192e-80

simplify31.0ms

Iterations

Iter	Nodes
done	53
1	53
0	38

end0.0ms

sample14.0s

Algorithm

intervals

Results

3.4s	2270×	body	5120	valid
2.8s	13371×	body	80	nan
2.3s	1749×	body	2560	valid
1.5s	6750×	body	80	valid
1.3s	970×	body	1280	valid
756.0ms	595×	body	10240	exit
253.0ms	480×	body	640	valid
81.0ms	227×	body	320	valid
27.0ms	110×	body	160	valid