Details

sample30.0ms

Algorithm

intervals

Results

12.0ms

322×

body

valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
10	4396
9	979
8	302
7	116
6	82
5	64
4	51
3	32
2	18
1	11
0	7

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ y (/ (- x (* x y)) z))
0.0b	(- x (* x y))
3.6b	(/ (- x (* x y)) z)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `div-sub` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `associate-+r-` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `flip-+` `div-inv` `distribute-lft-out`

Counts

3 → 55

Calls

3 calls:

14.0ms	(+ y (/ (- x (* x y)) z))
4.0ms	(- x (* x y))
11.0ms	(/ (- x (* x y)) z)

series146.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(+ y (/ (- x (* x y)) z))
58.0ms	(- x (* x y))
52.0ms	(/ (- x (* x y)) z)

simplify604.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
2	1038
1	242
0	94

prune305.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- x (* x y))) z)
0.2b	(* (sqrt (- x (* x y))) (/ (sqrt (- x (* x y))) z))
1.9b	(sqrt (- x (* x y)))
1.9b	(sqrt (- x (* x y)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`times-frac`
36×	`*-un-lft-identity` `add-cube-cbrt`
35×	`sqrt-prod`
22×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-div`
8×	`pow1`
6×	`associate-l` `associate-/l*` `unswap-sqr`
5×	`flip3--` `flip--`
4×	`add-log-exp`
3×	`associate-/r*`
2×	`frac-times` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 123

Calls

4 calls:

10.0ms	(/ (sqrt (- x (* x y))) z)
51.0ms	(* (sqrt (- x (* x y))) (/ (sqrt (- x (* x y))) z))
4.0ms	(sqrt (- x (* x y)))
4.0ms	(sqrt (- x (* x y)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (sqrt (- x (* x y))) z)
290.0ms	(* (sqrt (- x (* x y))) (/ (sqrt (- x (* x y))) z))
69.0ms	(sqrt (- x (* x y)))
74.0ms	(sqrt (- x (* x y)))

simplify3.3s

Counts

135 → 135

Iterations

Iter	Nodes
done	5001
2	3240
1	432
0	174

prune583.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 3.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* (/ 1 (sqrt z)) (/ (- x (* x y)) (sqrt z))))
0.2b	(/ 1 (sqrt z))
1.3b	(* (/ 1 (sqrt z)) (/ (- x (* x y)) (sqrt z)))
1.7b	(/ (- x (* x y)) (sqrt z))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
94×	`times-frac`
66×	`*-un-lft-identity`
60×	`add-cube-cbrt`
53×	`sqrt-prod`
32×	`add-exp-log`
22×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`unswap-sqr`
12×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `prod-exp`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod` `div-inv`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`frac-times` `+-commutative` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+` `flip--` `inv-pow`

Counts

4 → 181

Calls

4 calls:

10.0ms	(+ y (* (/ 1 (sqrt z)) (/ (- x (* x y)) (sqrt z))))
11.0ms	(/ 1 (sqrt z))
63.0ms	(* (/ 1 (sqrt z)) (/ (- x (* x y)) (sqrt z)))
12.0ms	(/ (- x (* x y)) (sqrt z))

series247.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(+ y (* (/ 1 (sqrt z)) (/ (- x (* x y)) (sqrt z))))
39.0ms	(/ 1 (sqrt z))
52.0ms	(* (/ 1 (sqrt z)) (/ (- x (* x y)) (sqrt z)))
81.0ms	(/ (- x (* x y)) (sqrt z))

simplify2.4s

Counts

193 → 193

Iterations

Iter	Nodes
done	5000
2	4998
1	752
0	257

prune847.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 2.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt z) y)
0.2b	(/ 1 (sqrt z))
1.3b	(* (/ 1 (sqrt z)) (- (/ x (sqrt z)) (/ x (/ (sqrt z) y))))
2.0b	(/ x (/ (sqrt z) y))

rewrite465.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
184×	`add-sqr-sqrt`
135×	`*-un-lft-identity`
125×	`add-cube-cbrt`
78×	`sqrt-prod`
31×	`associate-/r*`
24×	`add-exp-log`
22×	`associate-l`
20×	`associate-r`
18×	`add-cbrt-cube`
12×	`associate-/l*` `difference-of-squares`
10×	`div-inv`
8×	`pow1` `div-exp`
6×	`cbrt-undiv`
5×	`distribute-lft-out--` `unswap-sqr`
4×	`prod-exp` `add-log-exp`
3×	`frac-times` `clear-num` `frac-2neg` `associate-*r/` `pow-flip`
2×	`distribute-rgt-in` `rec-exp` `sub-neg` `distribute-lft-in` `flip3--` `1-exp` `frac-sub` `cbrt-unprod` `flip--`
1×	`sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `inv-pow`

Counts

4 → 263

Calls

4 calls:

5.0ms	(/ (sqrt z) y)
6.0ms	(/ 1 (sqrt z))
421.0ms	(* (/ 1 (sqrt z)) (- (/ x (sqrt z)) (/ x (/ (sqrt z) y))))
20.0ms	(/ x (/ (sqrt z) y))

series286.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (sqrt z) y)
31.0ms	(/ 1 (sqrt z))
116.0ms	(* (/ 1 (sqrt z)) (- (/ x (sqrt z)) (/ x (/ (sqrt z) y))))
66.0ms	(/ x (/ (sqrt z) y))

simplify584.0ms

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1173
0	417

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes275.0ms

Accuracy

61.4% (1.0b remaining)

Error of 1.9b against oracle of 0.9b and baseline of 3.4b

bsearch46.0ms

Steps

Iters	Range		Point
9	5.536000884157053e+42	2.608500637638846e+49	1.0103671538087413e+46

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

582.0ms

10107×

body

valid