Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	26
1	283	26
2	1620	26
3	5003	26

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.8b	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
44.5b	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
54×	`flip3-+` `flip-+`
50×	`associate-/r/`
44×	`add-sqr-sqrt`
36×	`frac-times`
30×	`associate-*r/`
28×	`add-cube-cbrt` `*-un-lft-identity`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
18×	`associate-*l/`
16×	`pow1`
14×	`associate-/l*` `difference-of-squares`
9×	`associate-/l/`
7×	`div-inv`
6×	`associate-r`
5×	`associate-/r*`
4×	`associate-l` `pow-prod-down` `add-log-exp`
3×	`swap-sqr`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `pow-sqr` `pow-prod-up` `flip--` `unswap-sqr`

Counts

4 → 200

Calls

4 calls:

72.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
51.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
115.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
69.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
26.0ms	(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
354.0ms	(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
64.0ms	(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify75.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1249	5670
1	5001	5161

prune2.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 34.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.3b	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite693.0ms

Algorithm

rewrite-expression-head

Rules

366×	`times-frac`
300×	`add-sqr-sqrt`
235×	`*-un-lft-identity`
155×	`add-cube-cbrt`
96×	`associate-r`
70×	`add-exp-log` `add-cbrt-cube`
62×	`difference-of-squares`
44×	`associate-/r/`
42×	`associate-l`
33×	`cbrt-undiv` `div-exp`
31×	`sqrt-prod` `distribute-lft-out--`
22×	`flip3-+` `flip-+` `div-inv`
19×	`associate-/l*`
16×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
9×	`distribute-lft-out`
6×	`pow1` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `clear-num`
2×	`flip3--` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 364

Calls

4 calls:

134.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
442.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
63.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
462.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
21.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
30.0ms	(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify115.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1683	10749
1	5001	9903

prune4.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 34.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.8b	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
35.2b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.2b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite443.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log` `add-cbrt-cube`
58×	`times-frac`
48×	`*-un-lft-identity`
42×	`associate-l`
39×	`add-sqr-sqrt`
38×	`cbrt-undiv` `div-exp`
29×	`prod-exp` `cbrt-unprod`
28×	`add-cube-cbrt`
14×	`associate-/r/`
12×	`associate-r`
9×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`pow1`
7×	`sqrt-prod` `div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r/` `associate-/r`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`frac-times` `flip3--` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--`

Counts

4 → 155

Calls

4 calls:

395.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
34.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

468.0ms	(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
19.0ms	(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
17.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
17.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify61.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1076	4948
1	5001	3682

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 34.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
0.1b	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.2b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.2b	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite468.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log` `add-cbrt-cube`
49×	`add-sqr-sqrt`
36×	`associate-r`
34×	`prod-exp` `cbrt-unprod`
33×	`cbrt-undiv` `div-exp`
32×	`times-frac`
29×	`*-un-lft-identity`
25×	`add-cube-cbrt`
24×	`sqrt-prod`
16×	`associate-l`
10×	`pow1`
8×	`sqrt-div`
7×	`unswap-sqr`
6×	`flip3-+` `associate-/r/` `flip-+`
4×	`add-log-exp`
3×	`frac-times` `associate-*l/` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `-commutative` `difference-of-squares`
1×	`flip3--` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 151

Calls

4 calls:

55.0ms	(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
398.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
3.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series546.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
481.0ms	(* (/ (* i (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
17.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
17.0ms	(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify60.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	995	4860
1	5001	3401

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.3b

regimes490.0ms

Accuracy

16.6% (13.1b remaining)

Error of 15.1b against oracle of 2.0b and baseline of 17.7b

bsearch131.0ms

Steps

Iters	Range		Point
7	2.4018236880003466e+173	1.6062481277728874e+175	2.506350120177012e+173
8	3.9706066004234025e+131	6.513110858803188e+135	4.812317256136544e+135
7	3.2582287631737085e+100	3.9752405492536297e+102	1.0563540889984321e+101
3	12838975.828019254	15571643.078997178	13009767.531205373
10	1.3305263721879182e-34	2.2070197894529602e-18	1.4040129120586976e-20

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	152
1	73	152
2	76	152
3	76	152

end0.0ms

sample1.2s

Algorithm

intervals

Results

708.0ms	8000×	body	80	valid
327.0ms	8000×	pre	80	true