Details

sample63.0ms

Algorithm

intervals

Results

18.0ms	220×	body	80	valid
7.0ms	17×	body	1280	valid
7.0ms	256×	pre	80	true
3.0ms	10×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	102	29
3	452	29
4	2090	29
done	5001	29

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.3b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b

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

1.3b

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

18.0b

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

323.0ms

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

1.0s

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

115.0ms

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

series917.0ms

Counts

3 → 9

Calls

3 calls:

382.0ms

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

403.0ms

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

131.0ms

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

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: 2 (515.0ms)

Iter	Nodes	Cost
0	225	4035
1	675	3821
2	2949	3577
done	5000	3577

prune509.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.1s

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-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

301.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
135.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
534.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

265.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
108.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
466.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
432.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify2.6s

Counts

307 → 307

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	385	9712
1	1051	9275
2	4615	8911
done	5001	8909

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.1b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.2b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
151×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
90×	`associate-r`
75×	`add-cube-cbrt`
22×	`distribute-lft-out`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
9×	`flip3-+` `flip-+`
7×	`pow1`
6×	`div-inv` `add-log-exp`
5×	`associate-/l*`
4×	`cbrt-undiv` `log-prod` `div-exp` `associate-l` `log-pow`
3×	`exp-prod` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-*l/` `associate-/l/`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

4 → 184

Calls

4 calls:

91.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
141.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
587.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
576.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
381.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
435.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
354.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify2.3s

Counts

196 → 196

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	325	5447
1	893	5140
2	3960	4794
done	5001	4792

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
2.1b	(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.1b	(log (exp (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.2b	(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

35×	`add-exp-log`
28×	`add-sqr-sqrt`
25×	`associate-r`
24×	`*-un-lft-identity`
23×	`add-cbrt-cube`
17×	`add-cube-cbrt`
15×	`times-frac`
14×	`prod-exp`
9×	`pow1` `div-exp` `associate-l`
8×	`cbrt-unprod`
6×	`add-log-exp`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`frac-times` `log-prod` `associate-*l/` `associate-/r/` `log-pow` `unswap-sqr`
3×	`exp-prod`
2×	`rec-exp` `flip3--` `1-exp` `associate-r/` `pow-prod-down` `-commutative` `flip--` `div-inv` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `exp-sum` `sum-log` `un-div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

191.0ms	(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
234.0ms	(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
931.0ms	(log (exp (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
598.0ms	(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series1.8s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
480.0ms	(+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
449.0ms	(log (exp (+ (* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
775.0ms	(* (+ alpha beta) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify2.0s

Counts

122 → 122

Iterations

Useful iterations: 2 (639.0ms)

Iter	Nodes	Cost
0	251	3505
1	684	3077
2	2879	2663
done	5002	2663

prune605.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

regimes293.0ms

Accuracy

72.1% (1.8b remaining)

Error of 7.5b against oracle of 5.8b and baseline of 12.1b

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	78
1	47	78
done	47	78

end0.0ms

sample2.0s

Algorithm

intervals

Results

585.0ms	6390×	body	80	valid
310.0ms	549×	body	640	valid
282.0ms	491×	body	1280	valid
276.0ms	8000×	pre	80	true
133.0ms	381×	body	320	valid
29.0ms	189×	body	160	valid