Details

sample442.0ms

Algorithm

intervals

Results

98.0ms	79×	body	5120	valid
91.0ms	434×	body	80	nan
73.0ms	49×	body	2560	valid
57.0ms	229×	body	80	valid
35.0ms	28×	body	10240	exit
34.0ms	25×	body	1280	valid
10.0ms	15×	body	640	valid
3.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify750.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
3	2006
2	280
1	59
0	21

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.4b

localize39.0ms

Local error

Found 4 expressions with local error:

14.3b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
14.3b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
15.9b	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M)))
25.8b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite164.0ms

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-l`
24×	`frac-add`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l/` `associate-r/`
14×	`associate-r`
13×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`pow1`
8×	`unswap-sqr`
6×	`add-log-exp`
4×	`insert-posit16` `div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `sum-log` `pow1/2` `sqrt-prod`

Counts

4 → 178

Calls

4 calls:

26.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
34.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
39.0ms	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M)))
61.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.7s

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
96.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
684.0ms	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M)))
800.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.5s

Counts

190 → 190

Iterations

Iter	Nodes
done	2001
2	2001
1	939
0	325

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 45.7b

localize59.0ms

Local error

Found 4 expressions with local error:

14.3b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
14.3b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
15.9b	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (/ (* c0 (/ (* (/ d D) (/ d D)) h)) w) M)))
28.2b	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (/ (* c0 (/ (* (/ d D) (/ d D)) h)) w) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite176.0ms

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-l`
24×	`frac-add`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`associate-l/` `associate-r/`
14×	`associate-r`
13×	`flip3-+` `flip-+`
12×	`flip3--` `flip--`
11×	`pow1`
8×	`unswap-sqr`
6×	`add-log-exp`
4×	`insert-posit16` `div-inv`
3×	`pow-prod-down`
2×	`sqrt-pow1` `*-commutative`
1×	`+-commutative` `sum-log` `pow1/2` `sqrt-prod`

Counts

4 → 178

Calls

4 calls:

45.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
29.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
51.0ms	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (/ (* c0 (/ (* (/ d D) (/ d D)) h)) w) M)))
47.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (/ (* c0 (/ (* (/ d D) (/ d D)) h)) w) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.6s

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
99.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
632.0ms	(sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (/ (* c0 (/ (* (/ d D) (/ d D)) h)) w) M)))
784.0ms	(+ (sqrt (* (+ M (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (- (/ (* c0 (/ (* (/ d D) (/ d D)) h)) w) M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify1.2s

Counts

190 → 190

Iterations

Iter	Nodes
done	2001
2	2001
1	952
0	328

prune1.5s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 44.0b

localize46.0ms

Local error

Found 4 expressions with local error:

14.3b	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
14.3b	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
15.9b	(sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M)))
25.8b	(+ (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))))

rewrite710.0ms

Algorithm

rewrite-expression-head

Rules

3744×	`times-frac`
1678×	`add-sqr-sqrt`
1547×	`*-un-lft-identity` `add-cube-cbrt`
1154×	`associate-r`
196×	`div-inv`
134×	`add-cbrt-cube` `add-exp-log`
74×	`cbrt-undiv` `div-exp`
28×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
26×	`associate-l`
9×	`pow1`
8×	`sqrt-div`
6×	`frac-add` `add-log-exp`
4×	`frac-times` `flip3--` `associate-l/` `associate-r/` `sqrt-prod` `insert-posit16` `flip--`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `difference-of-squares`

Counts

4 → 1325

Calls

4 calls:

65.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
69.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
215.0ms	(sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M)))
263.0ms	(+ (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))))

series1.1s

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
97.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
388.0ms	(sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M)))
511.0ms	(+ (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))))

simplify3.1s

Counts

1337 → 1337

Iterations

Iter	Nodes
done	2001
1	2001
0	1441

prune13.1s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 21.5b

localize26.0ms

Local error

Found 1 expressions with local error:

6.9b	(* (/ c0 w) (/ (exp (log 0)) 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
34×	`times-frac`
22×	`associate-r`
21×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-l`
11×	`log-prod` `exp-sum` `add-exp-log`
6×	`unswap-sqr`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
3×	`pow1`
2×	`div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `insert-posit16` `add-log-exp`

Counts

1 → 62

Calls

1 calls:

30.0ms

(* (/ c0 w) (/ (exp (log 0)) 2))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(* (/ c0 w) (/ (exp (log 0)) 2))

simplify7.2s

Counts

65 → 65

Iterations

Iter	Nodes
done	2723
4	2723
3	1043
2	551
1	387
0	140

prune328.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 19.5b

regimes2.1s

Accuracy

-1% (10.0b remaining)

Error of 34.5b against oracle of 24.4b and baseline of 34.4b

bsearch1.1s

Steps

Iters	Range		Point
9	3.522734515907261e-145	3.294025148135913e-139	9.213056584041128e-145
9	-3.034627296389685e-213	-7.422533325603152e-219	-7.401275573314534e-214

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample20.2s

Algorithm

intervals

Results

6.0s	2289×	body	5120	valid
3.5s	13246×	body	80	nan
3.2s	1689×	body	2560	valid
2.2s	6836×	body	80	valid
1.7s	610×	body	10240	exit
1.3s	939×	body	1280	valid
546.0ms	444×	body	640	valid
545.0ms	224×	body	320	valid
47.0ms	112×	body	160	valid