Details

sample366.0ms

Algorithm

intervals

Results

92.0ms	430×	body	80	nan
63.0ms	50×	body	2560	valid
57.0ms	69×	body	5120	valid
25.0ms	227×	body	80	valid
17.0ms	31×	body	1280	valid
14.0ms	15×	body	10240	exit
4.0ms	7×	body	640	valid
3.0ms	10×	body	320	valid
2.0ms	9×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	21	52
1	59	52
2	289	52
3	3227	52
done	5000	46

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 57.5b

localize27.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
24.6b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite983.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 143

Calls

4 calls:

43.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
53.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
67.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
807.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
114.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
148.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
302.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.2s

Counts

155 → 155

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	157	4688
1	468	4293
2	3049	2845
done	5001	2809

prune578.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 32.4b

localize12.0ms

Local error

Found 1 expressions with local error:

4.9b	(* (/ c0 (* 2.0 w)) 0)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
7×	`associate-l`
6×	`add-sqr-sqrt`
4×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
3×	`pow1` `times-frac` `associate-r`
2×	`cbrt-undiv` `div-exp`
1×	`mul0` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `add-log-exp` `unswap-sqr`

Counts

1 → 28

Calls

1 calls:

48.0ms

(* (/ c0 (* 2.0 w)) 0)

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (/ c0 (* 2.0 w)) 0)

simplify3.2s

Counts

31 → 31

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	67	283
1	158	74
2	472	38
3	2113	38
done	5000	38

prune149.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 30.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.5b	(* (cbrt c0) (cbrt c0))
0.6b	(cbrt c0)
0.6b	(cbrt c0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

22×	`cbrt-prod`
21×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`add-exp-log`
4×	`unswap-sqr`
3×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 62

Calls

3 calls:

22.0ms	(* (cbrt c0) (cbrt c0))
2.0ms	(cbrt c0)
2.0ms	(cbrt c0)

series867.0ms

Counts

3 → 9

Calls

3 calls:

319.0ms	(* (cbrt c0) (cbrt c0))
246.0ms	(cbrt c0)
301.0ms	(cbrt c0)

simplify5.5s

Counts

71 → 71

Iterations

Useful iterations: done (5.5s)

Iter	Nodes	Cost
0	61	459
1	115	360
2	319	342
3	1092	327
4	4427	322
done	5001	314

prune274.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.8b

localize64.0ms

Local error

Found 4 expressions with local error:

16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
16.4b	(/ (* c0 (* d d)) (* (* w h) (* D D)))
17.0b	(/ (* (* w h) (* D D)) (* c0 (* d d)))
26.6b	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
117×	`prod-exp` `cbrt-unprod`
45×	`cbrt-undiv` `div-exp`
6×	`*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
3×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`
2×	`sqrt-div` `frac-add`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

4 → 143

Calls

4 calls:

80.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
76.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
57.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
1.4s	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

series879.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
154.0ms	(/ (* c0 (* d d)) (* (* w h) (* D D)))
168.0ms	(/ (* (* w h) (* D D)) (* c0 (* d d)))
423.0ms	(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ 1 (/ (* (* w h) (* D D)) (* c0 (* d d)))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))

simplify2.8s

Counts

155 → 155

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	203	4744
1	602	4449
2	4316	2879
done	5001	2811

prune371.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.7b

regimes543.0ms

Accuracy

0% (2.3b remaining)

Error of 33.6b against oracle of 31.3b and baseline of 33.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	8	9
done	8	9

end0.0ms

sample14.3s

Algorithm

intervals

Results

3.6s	2264×	body	5120	valid
3.0s	6804×	body	80	valid
2.2s	13225×	body	80	nan
1.5s	1710×	body	2560	valid
753.0ms	613×	body	10240	exit
614.0ms	943×	body	1280	valid
253.0ms	445×	body	640	valid
79.0ms	228×	body	320	valid
28.0ms	107×	body	160	valid