Details

sample499.0ms

Algorithm

intervals

Results

127.0ms	65×	body	5120	valid
91.0ms	66×	body	2560	valid
78.0ms	421×	body	80	nan
59.0ms	202×	body	80	valid
56.0ms	28×	body	1280	valid
24.0ms	16×	body	10240	exit
8.0ms	12×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	4×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.6b

localize64.0ms

Local error

Found 4 expressions with local error:

12.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
12.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
12.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
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)))

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

172×	`add-cbrt-cube` `add-exp-log`
72×	`cbrt-undiv` `div-exp`
63×	`add-sqr-sqrt`
60×	`prod-exp` `cbrt-unprod`
48×	`times-frac`
39×	`associate-l`
33×	`*-un-lft-identity` `add-cube-cbrt`
21×	`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` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `difference-of-squares`

Counts

4 → 216

Calls

4 calls:

51.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
35.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
57.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
1.7s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series978.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
107.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
122.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
633.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.4s

Counts

228 → 228

Iterations

Iter	Nodes
done	5007
2	3007
1	697
0	217

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 26.9b

localize9.0ms

Local error

Found 1 expressions with local error:

4.7b	(* (/ c0 w) (/ 0 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`times-frac`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`pow1`
2×	`div-inv`
1×	`expm1-log1p-u` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 53

Calls

1 calls:

23.0ms

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

series8.0ms

Counts

1 → 3

Calls

1 calls:

8.0ms

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

simplify15.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5015
3	1300
2	492
1	278
0	112

prune299.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 25.5b

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

prune99.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 25.5b

localize84.0ms

Local error

Found 4 expressions with local error:

12.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
12.9b	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
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)))
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)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

116×	`add-cbrt-cube` `add-exp-log`
48×	`cbrt-undiv` `div-exp`
46×	`add-sqr-sqrt`
40×	`prod-exp` `cbrt-unprod`
32×	`times-frac`
26×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
14×	`fma-def` `associate-r`
12×	`sqrt-div` `frac-add`
8×	`pow1` `sqrt-prod` `add-log-exp` `unswap-sqr`
6×	`frac-times` `flip3--` `associate-l/` `associate-r/` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
2×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+` `difference-of-squares`

Counts

4 → 180

Calls

4 calls:

59.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
52.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
1.4s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
1.6s	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

series1.4s

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
131.0ms	(* (/ c0 w) (/ (* (/ d D) (/ d D)) h))
547.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))
626.0ms	(+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)))

simplify2.2s

Counts

192 → 192

Iterations

Iter	Nodes
done	5007
2	3007
1	697
0	217

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 25.5b

regimes1.0s

Accuracy

-7.9% (9.3b remaining)

Error of 34.2b against oracle of 24.9b and baseline of 33.5b

bsearch1.5s

Steps

Iters	Range	Point
10	1.5243080527895116e+137	2.388847055381767e+149	2.4030601747568853e+137
8	3.42389030945448e+56	1.6116351484409986e+61	9.618603368031972e+60
10	-1.741413259132783e+186	-1.2939187522739444e+170	-1.1564613338875407e+184

Iters

Range

Point

1.5243080527895116e+137

2.388847055381767e+149

2.4030601747568853e+137

3.42389030945448e+56

1.6116351484409986e+61

9.618603368031972e+60

-1.741413259132783e+186

-1.2939187522739444e+170

-1.1564613338875407e+184

simplify20.0ms

Iterations

Iter	Nodes
done	49
1	49
0	41

end0.0ms

sample20.5s

Algorithm

intervals

Results

5.9s	2326×	body	5120	valid
4.1s	13133×	body	80	nan
3.4s	1716×	body	2560	valid
2.2s	6674×	body	80	valid
1.3s	916×	body	1280	valid
1.2s	603×	body	10240	exit
941.0ms	438×	body	640	valid
211.0ms	221×	body	320	valid
54.0ms	116×	body	160	valid