Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

274×

body

valid

simplify104.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	117
6	117
5	112
4	88
3	59
2	37
1	21
0	9

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.8b

localize23.0ms

Local error

Found 2 expressions with local error:

3.4b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.2b	(* y (+ 1.0 (* z z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `clear-num` `associate-/r` `frac-2neg` `distribute-lft-in` `pow-prod-down` `-commutative` `unswap-sqr` `associate-/l/`

Counts

2 → 70

Calls

2 calls:

26.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
25.0ms	(* y (+ 1.0 (* z z)))

series151.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
82.0ms	(* y (+ 1.0 (* z z)))

simplify1.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
2	2223
1	439
0	156

prune422.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (* (/ y 1.0) (* (+ 1.0 (* z z)) x)))
2.3b	(* (/ y 1.0) (* (+ 1.0 (* z z)) x))
4.0b	(* (+ 1.0 (* z z)) x)

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
35×	`add-cbrt-cube`
25×	`prod-exp`
18×	`div-exp`
16×	`add-sqr-sqrt` `pow1` `associate-l`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`cbrt-unprod`
12×	`times-frac` `associate-*l/`
9×	`cbrt-undiv`
7×	`pow-prod-down`
5×	`rec-exp` `flip3-+` `1-exp` `associate-/r/` `flip-+`
4×	`frac-times` `associate-r` `associate-*r/`
3×	`pow-flip` `associate-/l*` `add-log-exp`
2×	`*-commutative` `div-inv`
1×	`clear-num` `associate-/r*` `frac-2neg` `inv-pow` `unswap-sqr`

Counts

3 → 103

Calls

3 calls:

80.0ms	(/ 1 (* (/ y 1.0) (* (+ 1.0 (* z z)) x)))
52.0ms	(* (/ y 1.0) (* (+ 1.0 (* z z)) x))
14.0ms	(* (+ 1.0 (* z z)) x)

series234.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ 1 (* (/ y 1.0) (* (+ 1.0 (* z z)) x)))
96.0ms	(* (/ y 1.0) (* (+ 1.0 (* z z)) x))
38.0ms	(* (+ 1.0 (* z z)) x)

simplify1.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
2	3191
1	564
0	184

prune550.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

localize27.0ms

Local error

Found 2 expressions with local error:

2.5b	(/ (* (/ 1 y) 1.0) (* (+ 1.0 (* z z)) x))
4.0b	(* (+ 1.0 (* z z)) x)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
25×	`add-cbrt-cube`
14×	`div-exp` `prod-exp`
8×	`cbrt-undiv` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`associate-*l/`
4×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`associate-r` `associate-l`
2×	`rec-exp` `flip3-+` `1-exp` `associate-/r/` `flip-+` `add-log-exp`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `pow-prod-down` `-commutative` `div-inv` `associate-/l*` `unswap-sqr` `associate-/l/`

Counts

2 → 52

Calls

2 calls:

17.0ms	(/ (* (/ 1 y) 1.0) (* (+ 1.0 (* z z)) x))
24.0ms	(* (+ 1.0 (* z z)) x)

series188.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(/ (* (/ 1 y) 1.0) (* (+ 1.0 (* z z)) x))
69.0ms	(* (+ 1.0 (* z z)) x)

simplify1.3s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
2	2910
1	405
0	127

prune282.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 2.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (/ y 1.0) (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ (pow z 2) 1.0)) x))))
2.3b	(* (/ y 1.0) (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ (pow z 2) 1.0)) x)))
16.1b	(sqrt (+ 1.0 (* z z)))
16.1b	(sqrt (+ (pow z 2) 1.0))

rewrite704.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-exp-log`
54×	`add-cbrt-cube`
52×	`sqrt-div`
48×	`prod-exp`
34×	`associate-*l/`
32×	`frac-times`
26×	`flip3-+` `div-exp` `flip-+`
25×	`pow1`
24×	`associate-*r/` `cbrt-unprod`
17×	`add-sqr-sqrt` `*-un-lft-identity` `associate-/r/`
15×	`add-cube-cbrt`
13×	`cbrt-undiv` `associate-l`
12×	`times-frac` `pow-prod-down`
7×	`rec-exp` `1-exp` `sqrt-prod`
4×	`pow-flip` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `distribute-lft-out` `inv-pow`

Counts

4 → 152

Calls

4 calls:

429.0ms	(/ 1 (* (/ y 1.0) (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ (pow z 2) 1.0)) x))))
229.0ms	(* (/ y 1.0) (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ (pow z 2) 1.0)) x)))
15.0ms	(sqrt (+ 1.0 (* z z)))
22.0ms	(sqrt (+ (pow z 2) 1.0))

series235.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ 1 (* (/ y 1.0) (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ (pow z 2) 1.0)) x))))
66.0ms	(* (/ y 1.0) (* (sqrt (+ 1.0 (* z z))) (* (sqrt (+ (pow z 2) 1.0)) x)))
49.0ms	(sqrt (+ 1.0 (* z z)))
46.0ms	(sqrt (+ (pow z 2) 1.0))

simplify1.6s

Counts

164 → 164

Iterations

Iter	Nodes
done	5001
2	4001
1	823
0	286

prune980.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 2.8b

regimes923.0ms

Accuracy

66.8% (1.5b remaining)

Error of 3.4b against oracle of 1.9b and baseline of 6.4b

bsearch2.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample957.0ms

Algorithm

intervals

Results

573.0ms

8615×

body

valid