Details

sample74.0ms

Algorithm

intervals

Results

17.0ms	194×	body	80	valid
9.0ms	20×	body	1280	valid
8.0ms	22×	body	640	valid
7.0ms	256×	pre	80	true
4.0ms	15×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
4	2146
3	448
2	97
1	31
0	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b

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

1.2b

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

20.8b

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

rewrite841.0ms

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:

162.0ms

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

625.0ms

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

49.0ms

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

series888.0ms

Counts

3 → 9

Calls

3 calls:

362.0ms

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

414.0ms

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

111.0ms

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

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5016
2	3101
1	690
0	225

prune697.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize104.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
0.1b	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
1.2b	(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
1.9b	(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

rewrite2.7s

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
62×	`*-un-lft-identity` `times-frac`
42×	`associate-l`
38×	`add-cube-cbrt`
36×	`associate-r`
28×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
6×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
5×	`flip3-+` `flip-+`
4×	`div-inv`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `cube-unmult` `pow3` `sum-cubes` `flip--`

Counts

4 → 150

Calls

4 calls:

279.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
309.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
2.1s	(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
8.0ms	(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

series9.9s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
360.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
8.8s	(+ (* (* 1.0 1.0) 1.0) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))
405.0ms	(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

simplify2.6s

Counts

162 → 162

Iterations

Iter	Nodes
done	5001
2	3232
1	730
0	217

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize197.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
0.2b	(* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))))))
1.2b	(log (* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))))
1.9b	(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
31×	`times-frac`
24×	`associate-l`
23×	`add-cube-cbrt`
21×	`associate-r`
18×	`add-cbrt-cube`
17×	`add-exp-log`
11×	`pow1`
6×	`prod-exp` `add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`cbrt-undiv` `div-exp` `associate-/r/`
3×	`pow-prod-down` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
2×	`flip3-+` `rem-log-exp` `log-pow` `*-commutative` `flip-+` `div-inv`
1×	`frac-times` `log-prod` `sub-neg` `flip3--` `diff-log` `associate-l/` `associate-r/` `flip--`

Counts

4 → 105

Calls

4 calls:

367.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
58.0ms	(* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))))))
36.0ms	(log (* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))))
4.0ms	(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

series54.3s

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))
21.6s	(* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i))))))))
31.8s	(log (* (exp (* (* 1.0 1.0) 1.0)) (exp (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))) (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))))))
435.0ms	(- 1.0 (* (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (/ (+ alpha beta) (+ (+ 2.0 (+ alpha beta)) (* 2.0 i)))))

simplify2.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5007
2	3015
1	736
0	240

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.6b	(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.6b	(cbrt (+ (+ alpha beta) (* 2.0 i)))
9.9b	(+ (* (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+`
3×	`pow1/3`
1×	`+-commutative` `sum-log`

Counts

4 → 50

Calls

4 calls:

12.0ms	(cbrt (+ (+ alpha beta) (* 2.0 i)))
21.0ms	(cbrt (+ (+ alpha beta) (* 2.0 i)))
22.0ms	(cbrt (+ (+ alpha beta) (* 2.0 i)))
351.0ms	(+ (* (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt (+ (+ alpha beta) (* 2.0 i)))
219.0ms	(cbrt (+ (+ alpha beta) (* 2.0 i)))
223.0ms	(cbrt (+ (+ alpha beta) (* 2.0 i)))
484.0ms	(+ (* (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify3.4s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	4454
2	995
1	303
0	110

prune626.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

regimes913.0ms

Accuracy

74.7% (1.7b remaining)

Error of 7.4b against oracle of 5.7b and baseline of 12.3b

bsearch5.0ms

simplify23.0ms

Iterations

Iter	Nodes
done	62
1	62
0	46

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	6390×	body	80	valid
267.0ms	8000×	pre	80	true
239.0ms	522×	body	1280	valid
163.0ms	539×	body	640	valid
113.0ms	350×	body	320	valid
31.0ms	199×	body	160	valid