Details

sample101.0ms

Algorithm

intervals

Results

38.0ms	199×	body	80	valid
16.0ms	21×	body	1280	valid
13.0ms	22×	body	640	valid
11.0ms	256×	pre	80	true
3.0ms	8×	body	320	valid
2.0ms	6×	body	160	valid

simplify626.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize50.0ms

Local error

Found 3 expressions with local error:

20.8b

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

1.9b

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

0.1b

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

rewrite732.0ms

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--` `insert-posit16` `flip--`
2×	`clear-num` `frac-2neg` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 114

Calls

3 calls:

Slowest

489.0ms

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

201.0ms

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

38.0ms

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

series953.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

478.0ms

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

337.0ms

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

137.0ms

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

simplify1.5s

Counts: 123 → 123

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize72.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.6b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l` `insert-posit16`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 299

Calls

4 calls:

Slowest

354.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
147.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
91.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
30.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

348.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
260.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
248.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
124.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

simplify1.9s

Counts: 311 → 311

prune5.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize60.0ms

Local error

Found 4 expressions with local error:

3.4b	(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
0.2b	(* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
0.1b	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

rewrite999.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
50×	`add-exp-log`
43×	`times-frac`
39×	`associate-r`
32×	`add-cbrt-cube` `add-cube-cbrt`
22×	`prod-exp`
12×	`div-exp` `cbrt-unprod`
11×	`frac-times` `pow1` `associate-*l/`
10×	`flip3-+` `flip-+`
7×	`cbrt-undiv` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
5×	`associate-l` `associate-/l*`
4×	`pow-prod-down` `associate-*r/` `insert-posit16` `distribute-lft-out`
3×	`rec-exp` `associate-/r*` `1-exp` `div-inv`
2×	`*-commutative` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-sub` `un-div-inv` `flip--`

Counts

4 → 159

Calls

4 calls:

Slowest

531.0ms	(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
298.0ms	(* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
116.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))
52.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))

series812.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

357.0ms	(* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
221.0ms	(+ (* (* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)
135.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
100.0ms	(* (+ beta alpha) (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))))

simplify1.4s

Counts: 171 → 171

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize51.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
0.1b	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
0.1b	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.0b	(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))

rewrite882.0ms

Algorithm

rewrite-expression-head

Rules

1250×	`times-frac`
1055×	`*-un-lft-identity`
619×	`add-sqr-sqrt`
461×	`add-cube-cbrt`
218×	`distribute-lft-out`
96×	`associate-/l*`
79×	`distribute-lft-out--` `difference-of-squares`
60×	`associate-/r/`
33×	`div-inv`
30×	`associate-/r*`
26×	`flip3--` `flip--`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1` `flip3-+` `flip-+` `insert-posit16`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

4 → 649

Calls

4 calls:

Slowest

546.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
157.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
105.0ms	(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
44.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

series936.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

390.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)
286.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
154.0ms	(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
105.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))

simplify1.3s

Counts: 661 → 661

prune10.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

regimes463.0ms

Accuracy

15.2% (5.7b remaining)

Error of 11.6b against oracle of 5.9b and baseline of 12.6b

bsearch194.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	6320×	body	80	valid
590.0ms	377×	body	320	valid
481.0ms	550×	body	640	valid
428.0ms	8000×	pre	80	true
423.0ms	554×	body	1280	valid
91.0ms	199×	body	160	valid