Details

sample70.0ms

Algorithm

intervals

Results

20.0ms	207×	body	80	valid
8.0ms	256×	pre	80	true
6.0ms	14×	body	1280	valid
6.0ms	16×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	8×	body	160	valid

simplify839.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize21.0ms

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))

2.7b

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

16.6b

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

rewrite1.1s

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:

247.0ms

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

782.0ms

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

104.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

613.0ms

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

373.0ms

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

96.0ms

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

simplify1.3s

Counts: 120 → 120

prune444.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.8b	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
484×	`*-un-lft-identity`
408×	`add-sqr-sqrt`
260×	`add-cube-cbrt`
219×	`sqrt-prod`
153×	`associate-r`
67×	`distribute-lft-out`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
34×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/l*`
21×	`flip3-+` `flip-+`
19×	`div-inv`
15×	`unswap-sqr`
14×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 485

Calls

4 calls:

274.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
958.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
192.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
232.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.3s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
296.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
161.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
468.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify1.2s

Counts: 497 → 497

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.8b	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
484×	`*-un-lft-identity`
408×	`add-sqr-sqrt`
260×	`add-cube-cbrt`
219×	`sqrt-prod`
153×	`associate-r`
67×	`distribute-lft-out`
45×	`distribute-lft-out--` `difference-of-squares`
38×	`associate-/r/`
34×	`associate-l`
32×	`add-exp-log` `add-cbrt-cube`
25×	`associate-/l*`
21×	`flip3-+` `flip-+`
19×	`div-inv`
15×	`unswap-sqr`
14×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
8×	`sqrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l/`
2×	`frac-2neg` `div-sub` `clear-num`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 485

Calls

4 calls:

303.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.1s	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
233.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
229.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

370.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
407.0ms	(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
200.0ms	(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
468.0ms	(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify1.1s

Counts: 497 → 497

prune2.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b	(* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
7.5b	(+ (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite3.8s

Algorithm

rewrite-expression-head

Rules

2462×	`times-frac`
2250×	`sqrt-prod`
1939×	`*-un-lft-identity`
1392×	`add-sqr-sqrt`
989×	`add-cube-cbrt`
466×	`associate-l`
430×	`distribute-lft-out`
153×	`associate-r`
96×	`sqrt-div`
80×	`associate-/r/`
67×	`associate-/l*`
65×	`unswap-sqr`
50×	`add-exp-log` `add-cbrt-cube`
45×	`distribute-lft-out--` `difference-of-squares`
41×	`flip3-+` `flip-+`
40×	`div-inv`
24×	`cbrt-undiv` `div-exp`
17×	`associate-/r*`
9×	`prod-exp` `cbrt-unprod`
6×	`pow1` `add-log-exp`
2×	`frac-2neg` `div-sub` `clear-num` `associate-/l/`
1×	`+-commutative` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative`

Counts

4 → 1451

Calls

4 calls:

535.0ms	(/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
302.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.4s	(* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
384.0ms	(+ (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

251.0ms	(/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
367.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
379.0ms	(* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
455.0ms	(+ (* (/ (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify2.6s

Counts: 1463 → 1463

prune6.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

regimes341.0ms

Accuracy

-2.5% (6.5b remaining)

Error of 12.1b against oracle of 5.7b and baseline of 12.0b

bsearch304.0ms

Steps

Iters	Range		Point
5	1.473460923404379e+144	4.014811456694522e+144	2.9886245137939063e+144
5	3.267832712809978e+61	1.242812118712508e+62	4.27967945082249e+61
8	342065401322694.06	1.1289721806558901e+17	1154993415963887.2

simplify530.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	6410×	body	80	valid
314.0ms	559×	body	640	valid
265.0ms	507×	body	1280	valid
247.0ms	8000×	pre	80	true
87.0ms	336×	body	320	valid
32.0ms	188×	body	160	valid