Details

sample376.0ms

Algorithm

intervals

Results

120.0ms	82×	body	5120	valid
79.0ms	480×	body	80	nan
35.0ms	46×	body	2560	valid
32.0ms	235×	body	80	valid
18.0ms	21×	body	10240	exit
17.0ms	30×	body	1280	valid
6.0ms	15×	body	640	valid
4.0ms	10×	body	320	valid
1.0ms	2×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5011
3	3014
2	286
1	60
0	21

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.2b

localize74.0ms

Local error

Found 4 expressions with local error:

12.0b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
12.0b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
13.3b	(* (/ c0 w) (/ (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) 2.0))
26.7b	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

rewrite6.0s

Algorithm

rewrite-expression-head

Rules

128×	`add-cbrt-cube` `add-exp-log`
70×	`add-sqr-sqrt`
54×	`times-frac`
52×	`cbrt-undiv` `div-exp`
44×	`prod-exp` `cbrt-unprod`
39×	`associate-l`
38×	`*-un-lft-identity` `add-cube-cbrt`
27×	`associate-r`
12×	`unswap-sqr`
10×	`pow1`
7×	`fma-def`
6×	`sqrt-div` `frac-add` `div-inv` `add-log-exp`
5×	`frac-times` `associate-l/` `associate-r/`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `difference-of-squares`

Counts

4 → 202

Calls

4 calls:

64.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
67.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
4.1s	(* (/ c0 w) (/ (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) 2.0))
1.8s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.7s

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
148.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
878.0ms	(* (/ c0 w) (/ (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) 2.0))
590.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify3.1s

Counts

214 → 214

Iterations

Iter	Nodes
done	5001
2	4357
1	1001
0	296

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 28.1b

localize1.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune217.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 28.1b

localize89.0ms

Local error

Found 4 expressions with local error:

12.0b	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
12.0b	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
12.0b	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
26.7b	(+ (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))

rewrite4.5s

Algorithm

rewrite-expression-head

Rules

5616×	`times-frac`
2514×	`add-sqr-sqrt`
2319×	`*-un-lft-identity` `add-cube-cbrt`
1731×	`associate-r`
294×	`div-inv`
199×	`add-cbrt-cube` `add-exp-log`
111×	`cbrt-undiv` `div-exp`
42×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
39×	`associate-l`
10×	`pow1`
7×	`fma-def`
6×	`sqrt-div` `frac-add` `add-log-exp`
5×	`frac-times` `associate-l/` `associate-r/`
4×	`expm1-log1p-u` `sqrt-prod` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `difference-of-squares`

Counts

4 → 1964

Calls

4 calls:

308.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
330.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
307.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
3.2s	(+ (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
105.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
134.0ms	(* (/ c0 w) (/ (/ d D) (/ h (/ d D))))
719.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))

simplify2.9s

Counts

1976 → 1976

Iterations

Iter	Nodes
done	5000
0	1427

prune21.8s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 27.8b

localize139.0ms

Local error

Found 4 expressions with local error:

12.2b	(cbrt (/ d D))
12.2b	(cbrt (/ d D))
12.2b	(cbrt (/ d D))
33.1b	(+ (sqrt (- (* (* (/ (* c0 (* (cbrt (/ d D)) (cbrt (/ d D)))) w) (/ (/ d D) (/ h (cbrt (/ d D))))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))

rewrite7.0s

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
6×	`fma-def` `sqrt-div` `frac-add` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-div` `flip3--` `pow1/3` `sqrt-prod` `div-inv` `flip--`
2×	`frac-times` `associate-l/` `associate-r/`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 97

Calls

4 calls:

3.0ms	(cbrt (/ d D))
3.0ms	(cbrt (/ d D))
3.0ms	(cbrt (/ d D))
7.0s	(+ (sqrt (- (* (* (/ (* c0 (* (cbrt (/ d D)) (cbrt (/ d D)))) w) (/ (/ d D) (/ h (cbrt (/ d D))))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))

series711.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (/ d D))
90.0ms	(cbrt (/ d D))
115.0ms	(cbrt (/ d D))
402.0ms	(+ (sqrt (- (* (* (/ (* c0 (* (cbrt (/ d D)) (cbrt (/ d D)))) w) (/ (/ d D) (/ h (cbrt (/ d D))))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))))

simplify2.8s

Counts

109 → 109

Iterations

Iter	Nodes
done	5002
2	1507
1	414
0	169

prune1.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 27.8b

regimes2.7s

Accuracy

16% (8.0b remaining)

Error of 31.8b against oracle of 23.7b and baseline of 33.3b

bsearch5.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	31
1	31
0	25

end0.0ms

sample13.6s

Algorithm

intervals

Results

3.9s	2316×	body	5120	valid
2.8s	13093×	body	80	nan
2.3s	1727×	body	2560	valid
1.3s	6883×	body	80	valid
832.0ms	955×	body	1280	valid
614.0ms	582×	body	10240	exit
381.0ms	465×	body	640	valid
78.0ms	225×	body	320	valid
27.0ms	111×	body	160	valid