Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	30×	body	1280	valid
10.0ms	186×	body	80	valid
5.0ms	22×	body	640	valid
4.0ms	21×	body	320	valid
2.0ms	15×	body	160	valid

simplify56.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	78
6	78
5	76
4	65
3	40
2	22
1	12
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.7b

localize33.0ms

Local error

Found 3 expressions with local error:

0.1b	(* x (/ (sin y) y))
0.1b	(/ (sin y) y)
2.7b	(/ (* x (/ (sin y) y)) z)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`times-frac`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
6×	`cbrt-undiv` `associate-/r*` `div-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `associate-/l*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `associate-/l/`

Counts

3 → 89

Calls

3 calls:

21.0ms	(* x (/ (sin y) y))
7.0ms	(/ (sin y) y)
10.0ms	(/ (* x (/ (sin y) y)) z)

series250.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* x (/ (sin y) y))
39.0ms	(/ (sin y) y)
129.0ms	(/ (* x (/ (sin y) y)) z)

simplify1.6s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1179
1	344
0	145

prune552.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.6b	(cbrt z)
1.4b	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (cbrt z)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

152×	`times-frac`
110×	`add-sqr-sqrt`
82×	`associate-r`
78×	`*-un-lft-identity` `add-cube-cbrt`
52×	`cbrt-prod`
40×	`add-exp-log`
28×	`add-cbrt-cube`
15×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
10×	`unswap-sqr`
8×	`div-inv`
7×	`associate-l`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 170

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
1.0ms	(cbrt z)
117.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (cbrt z)))

series1.0s

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt z)
326.0ms	(cbrt z)
273.0ms	(cbrt z)
157.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (/ (sin y) y) (cbrt z)))

simplify3.0s

Counts

182 → 182

Iterations

Iter	Nodes
done	5002
2	4401
1	1077
0	310

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (/ x (* (cbrt z) (cbrt z))) (* (cbrt (/ (/ (sin y) y) (cbrt z))) (cbrt (/ (/ (sin y) y) (cbrt z)))))
2.3b	(cbrt (/ (/ (sin y) y) (cbrt z)))
2.3b	(cbrt (/ (/ (sin y) y) (cbrt z)))
2.3b	(cbrt (/ (/ (sin y) y) (cbrt z)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

400×	`times-frac`
363×	`cbrt-prod`
215×	`add-sqr-sqrt`
213×	`*-un-lft-identity` `add-cube-cbrt`
25×	`add-exp-log`
22×	`div-inv`
15×	`add-cbrt-cube`
11×	`cbrt-div` `prod-exp` `cbrt-unprod`
9×	`pow1`
7×	`associate-l`
5×	`frac-times` `associate-*r/`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `pow-prod-down` `associate-*l/`
2×	`unswap-sqr`
1×	`associate-r` `*-commutative`

Counts

4 → 320

Calls

4 calls:

102.0ms	(* (/ x (* (cbrt z) (cbrt z))) (* (cbrt (/ (/ (sin y) y) (cbrt z))) (cbrt (/ (/ (sin y) y) (cbrt z)))))
13.0ms	(cbrt (/ (/ (sin y) y) (cbrt z)))
14.0ms	(cbrt (/ (/ (sin y) y) (cbrt z)))
18.0ms	(cbrt (/ (/ (sin y) y) (cbrt z)))

series1.2s

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (/ x (* (cbrt z) (cbrt z))) (* (cbrt (/ (/ (sin y) y) (cbrt z))) (cbrt (/ (/ (sin y) y) (cbrt z)))))
271.0ms	(cbrt (/ (/ (sin y) y) (cbrt z)))
286.0ms	(cbrt (/ (/ (sin y) y) (cbrt z)))
286.0ms	(cbrt (/ (/ (sin y) y) (cbrt z)))

simplify2.3s

Counts

332 → 332

Iterations

Iter	Nodes
done	5001
2	1956
1	820
0	422

prune2.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.8b	(* (/ x (* (cbrt z) (cbrt z))) (/ (sin y) y))
1.0b	(/ (* (/ x (* (cbrt z) (cbrt z))) (/ (sin y) y)) (cbrt z))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
39×	`add-cbrt-cube`
29×	`add-sqr-sqrt`
22×	`times-frac`
21×	`cbrt-undiv` `div-exp`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`prod-exp` `cbrt-unprod`
13×	`associate-r`
12×	`cbrt-prod`
7×	`associate-l`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-inv` `associate-/l/`
2×	`frac-times` `pow1/3` `associate-l/` `associate-r/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 118

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
54.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (sin y) y))
36.0ms	(/ (* (/ x (* (cbrt z) (cbrt z))) (/ (sin y) y)) (cbrt z))

series787.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(cbrt z)
240.0ms	(cbrt z)
162.0ms	(* (/ x (* (cbrt z) (cbrt z))) (/ (sin y) y))
137.0ms	(/ (* (/ x (* (cbrt z) (cbrt z))) (/ (sin y) y)) (cbrt z))

simplify1.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5013
2	2166
1	572
0	199

prune563.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

regimes376.0ms

Accuracy

93.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 3.1b

bsearch67.0ms

Steps

Iters	Range		Point
4	66380113.15882991	110585599.62796573	67082210.61680344
9	-1.137268005656622e-18	-9.180461641993722e-25	-3.629406164941695e-19

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample2.2s

Algorithm

intervals

Results

880.0ms	5902×	body	80	valid
453.0ms	965×	body	1280	valid
377.0ms	1001×	body	640	valid
185.0ms	585×	body	320	valid
48.0ms	308×	body	160	valid