Details

sample394.0ms

Algorithm

intervals

Results

108.0ms	74×	body	5120	valid
71.0ms	227×	body	80	valid
50.0ms	405×	body	80	nan
41.0ms	52×	body	2560	valid
22.0ms	20×	body	10240	exit
14.0ms	24×	body	1280	valid
8.0ms	18×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 52.8b

localize104.0ms

Local error

Found 4 expressions with local error:

11.3b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
11.3b	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
16.3b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
24.9b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

rewrite243.0ms

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:

41.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
42.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
70.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
80.0ms	(+ (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:

115.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
98.0ms	(* (/ (* (/ d D) (/ d D)) h) (/ c0 w))
845.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
971.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

simplify2.8s

Counts

186 → 186

Iterations

Iter	Nodes
done	5000
2	4720
1	950
0	325

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 46.3b

localize147.0ms

Local error

Found 4 expressions with local error:

16.3b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
16.3b	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
24.9b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))
24.9b	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-div`
48×	`frac-times` `frac-add`
32×	`associate-l/` `associate-r/`
26×	`flip3-+` `flip-+`
24×	`flip3--` `flip--`
10×	`pow1`
8×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
2×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod`

Counts

4 → 108

Calls

4 calls:

63.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
40.0ms	(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)))
60.0ms	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

series4.4s

Counts

4 → 12

Calls

4 calls:

929.0ms	(sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M)))
1.4s	(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)))
1.0s	(+ (sqrt (* (+ M (* (/ (* (/ d D) (/ d D)) h) (/ c0 w))) (- (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)) M))) (* (/ (* (/ d D) (/ d D)) h) (/ c0 w)))

simplify2.5s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	1832
1	519
0	200

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 46.3b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2 (* (* h D) D))
5.6b	(* (* (/ 2 (* (* h D) D)) (/ (* (* c0 d) d) w)) (/ c0 w))
7.8b	(/ (* (* c0 d) d) w)
17.3b	(* (/ 2 (* (* h D) D)) (/ (* (* c0 d) d) w))

rewrite540.0ms

Algorithm

rewrite-expression-head

Rules

315×	`add-cbrt-cube` `add-exp-log`
160×	`prod-exp` `cbrt-unprod`
95×	`cbrt-undiv` `div-exp`
21×	`add-sqr-sqrt` `times-frac`
20×	`associate-r`
19×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
8×	`associate-l`
6×	`frac-times` `associate-*l/`
5×	`div-inv`
4×	`associate-/r` `pow-prod-down` `associate-r/` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 204

Calls

4 calls:

15.0ms	(/ 2 (* (* h D) D))
381.0ms	(* (* (/ 2 (* (* h D) D)) (/ (* (* c0 d) d) w)) (/ c0 w))
18.0ms	(/ (* (* c0 d) d) w)
113.0ms	(* (/ 2 (* (* h D) D)) (/ (* (* c0 d) d) w))

series522.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ 2 (* (* h D) D))
218.0ms	(* (* (/ 2 (* (* h D) D)) (/ (* (* c0 d) d) w)) (/ c0 w))
59.0ms	(/ (* (* c0 d) d) w)
213.0ms	(* (/ 2 (* (* h D) D)) (/ (* (* c0 d) d) w))

simplify1.3s

Counts

216 → 216

Iterations

Iter	Nodes
done	5001
1	1162
0	304

prune1.8s

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 37.9b

localize76.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (/ c0 (cbrt w)) (/ d (cbrt w)))
4.7b	(* (* (/ 2 D) (/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))) (/ d (cbrt w)))
5.6b	(* (* (* (/ 2 D) (/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))) (/ d (cbrt w))) (/ c0 w))
11.4b	(/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

1115×	`add-exp-log`
938×	`add-cbrt-cube`
537×	`prod-exp` `cbrt-unprod`
420×	`cbrt-undiv` `div-exp`
80×	`add-sqr-sqrt`
76×	`times-frac`
57×	`associate-r`
50×	`*-un-lft-identity` `add-cube-cbrt`
33×	`cbrt-prod`
24×	`frac-times` `associate-l` `associate-*l/`
20×	`pow1`
12×	`associate-*r/`
10×	`pow-prod-down`
9×	`unswap-sqr`
5×	`div-inv`
4×	`add-log-exp`
3×	`*-commutative` `associate-/l/`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-/l`

Counts

4 → 469

Calls

4 calls:

52.0ms	(* (/ c0 (cbrt w)) (/ d (cbrt w)))
218.0ms	(* (* (/ 2 D) (/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))) (/ d (cbrt w)))
756.0ms	(* (* (* (/ 2 D) (/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))) (/ d (cbrt w))) (/ c0 w))
33.0ms	(/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))

series1.1s

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (/ c0 (cbrt w)) (/ d (cbrt w)))
239.0ms	(* (* (/ 2 D) (/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))) (/ d (cbrt w)))
245.0ms	(* (* (* (/ 2 D) (/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))) (/ d (cbrt w))) (/ c0 w))
366.0ms	(/ (* (/ c0 (cbrt w)) (/ d (cbrt w))) (* D h))

simplify2.1s

Counts

481 → 481

Iterations

Iter	Nodes
done	5001
1	2800
0	661

prune3.6s

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 25.5b

regimes3.0s

Accuracy

-15.6% (20.2b remaining)

Error of 46.2b against oracle of 26.0b and baseline of 43.5b

bsearch609.0ms

Steps

Iters	Range	Point
9	6.138075045906368e-134	1.6008394440379539e-124	2.2890969237332912e-126
4	7.21341071147401e-185	1.2181911441445165e-184	1.0337907806102388e-184
7	1.9738675511904585e-281	1.6674727321023433e-279	3.347504912387466e-281

Iters

Range

Point

6.138075045906368e-134

1.6008394440379539e-124

2.2890969237332912e-126

7.21341071147401e-185

1.2181911441445165e-184

1.0337907806102388e-184

1.9738675511904585e-281

1.6674727321023433e-279

3.347504912387466e-281

simplify19.0ms

Iterations

Iter	Nodes
done	66
2	66
1	65
0	50

end0.0ms

sample14.0s

Algorithm

intervals

Results

2.8s	2343×	body	5120	valid
2.7s	13132×	body	80	nan
2.2s	1668×	body	2560	valid
1.3s	629×	body	10240	exit
1.2s	480×	body	640	valid
1.0s	6839×	body	80	valid
642.0ms	836×	body	1280	valid
499.0ms	89×	body	160	valid
86.0ms	239×	body	320	valid