Details

sample100.0ms

Algorithm

intervals

Results

29.0ms	210×	body	80	valid
29.0ms	256×	pre	80	true
8.0ms	14×	body	1280	valid
8.0ms	15×	body	640	valid
5.0ms	13×	body	320	valid
1.0ms	4×	body	160	valid

simplify713.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2155
3	440
2	95
1	32
0	16

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.1b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

1.3b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

21.1b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite589.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `flip--`
2×	`clear-num` `frac-2neg` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 111

Calls

3 calls:

105.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

442.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

40.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series823.0ms

Counts

3 → 9

Calls

3 calls:

334.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

371.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

118.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.1s

Counts

120 → 120

Iterations

Iter	Nodes
2	3007
1	696
0	225

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b	(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.1b	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
1.3b	(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

rewrite701.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
35×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
8×	`flip3-+` `flip-+`
7×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-l` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3--` `div-sub` `pow-prod-down` `*-commutative` `flip--`

Counts

4 → 129

Calls

4 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
172.0ms	(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
68.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
414.0ms	(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series800.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
341.0ms	(/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
118.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
247.0ms	(+ (/ (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

simplify1.1s

Counts

141 → 141

Iterations

Iter	Nodes
2	3008
1	683
0	223

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.2b	(* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.2b	(/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))
3.0b	(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite579.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
52×	`add-exp-log`
42×	`add-sqr-sqrt`
40×	`times-frac`
39×	`associate-r`
32×	`add-cbrt-cube`
31×	`add-cube-cbrt`
22×	`prod-exp`
13×	`div-exp`
12×	`pow1` `cbrt-unprod`
11×	`frac-times` `associate-*l/`
10×	`flip3-+` `flip-+`
8×	`distribute-lft-out`
7×	`cbrt-undiv`
6×	`associate-/r/` `add-log-exp`
5×	`associate-l`
4×	`rec-exp` `associate-/r` `1-exp` `pow-prod-down` `associate-r/`
3×	`div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `unswap-sqr`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 152

Calls

4 calls:

81.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
261.0ms	(* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
102.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))
133.0ms	(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series868.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
341.0ms	(* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
94.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))
294.0ms	(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.2s

Counts

164 → 164

Iterations

Iter	Nodes
2	3202
1	826
0	261

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.3b	(/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
1.3b	(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))) 1.0)

rewrite740.0ms

Algorithm

rewrite-expression-head

Rules

86×	`times-frac`
73×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
45×	`add-exp-log`
25×	`add-cbrt-cube` `associate-/r/`
22×	`div-exp`
21×	`associate-r`
16×	`associate-/r*`
13×	`flip3-+` `flip-+`
10×	`frac-times` `cbrt-undiv` `associate-*l/`
8×	`prod-exp` `div-inv` `associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`add-log-exp`
5×	`associate-*r/`
4×	`rec-exp` `1-exp` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `sum-log` `flip3--` `div-sub` `pow-prod-down` `*-commutative` `pow-flip` `flip--` `inv-pow`

Counts

4 → 182

Calls

4 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
88.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
133.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
467.0ms	(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))) 1.0)

series940.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
123.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
298.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))))
419.0ms	(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2 i)) 2.0) (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))))) 1.0)

simplify1.7s

Counts

194 → 194

Iterations

Iter	Nodes
2	3665
1	877
0	313

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

regimes498.0ms

Accuracy

72.7% (1.8b remaining)

Error of 7.5b against oracle of 5.7b and baseline of 12.3b

bsearch3.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	45
1	45
0	37

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.4s	6367×	body	80	valid
462.0ms	532×	body	1280	valid
434.0ms	8000×	pre	80	true
313.0ms	569×	body	640	valid
167.0ms	335×	body	320	valid
76.0ms	197×	body	160	valid