Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	201×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	19×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize12.0ms

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))

2.5b

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

20.3b

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

rewrite824.0ms

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:

185.0ms

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

580.0ms

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

55.0ms

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

series656.0ms

Counts

3 → 9

Calls

3 calls:

256.0ms

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

314.0ms

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

86.0ms

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

simplify89.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	681	1905
1	3622	1789
2	5003	1789

prune348.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
0.1b	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
2.5b	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.2s

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-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1` `flip3-+` `flip-+`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log`

Counts

4 → 645

Calls

4 calls:

79.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
221.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
60.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
796.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series798.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
265.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
89.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
314.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify147.0ms

Algorithm

egg-herbie

Counts

657 → 657

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1783	13720
1	5001	13481

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
0.1b	(* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.5b	(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
2.9b	(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite5.7s

Algorithm

rewrite-expression-head

Rules

9242×	`times-frac`
8907×	`*-un-lft-identity`
3667×	`add-sqr-sqrt`
2757×	`add-cube-cbrt`
2013×	`distribute-lft-out`
1008×	`swap-sqr`
625×	`distribute-lft-out--`
412×	`difference-of-squares`
366×	`unpow-prod-down` `cube-prod`
362×	`associate-r` `associate-l`
312×	`associate-/r/`
170×	`div-inv`
137×	`flip3--` `flip--`
94×	`add-exp-log` `add-cbrt-cube`
54×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod` `unswap-sqr`
12×	`pow1`
8×	`add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow-exp` `rem-cube-cbrt`
3×	`pow-unpow`
1×	`+-commutative` `cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `sub-neg` `pow-pow` `pow-plus` `diff-log` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `pow-sqr` `sum-cubes` `*-commutative` `pow-prod-up` `sqr-pow`

Counts

4 → 2578

Calls

4 calls:

250.0ms	(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
2.5s	(* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.1s	(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
375.0ms	(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series10.7s

Counts

4 → 12

Calls

4 calls:

3.5s	(pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
1.8s	(* (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
5.3s	(+ (pow (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))
204.0ms	(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify772.0ms

Algorithm

egg-herbie

Counts

2590 → 2590

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5002	95321

prune5.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
0.1b	(pow (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 3)
2.5b	(+ (* (pow (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 3) (pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)) (pow 1.0 3))
2.9b	(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

rewrite754.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
70×	`times-frac`
44×	`unpow-prod-down` `cube-prod`
42×	`add-cube-cbrt`
16×	`distribute-lft-out`
12×	`difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--`
8×	`associate-/r/` `add-log-exp`
6×	`pow1` `pow-unpow`
5×	`flip3-+` `flip-+`
4×	`pow-exp` `div-inv` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `sqr-pow`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `sum-log` `sum-cubes` `flip--`

Counts

4 → 157

Calls

4 calls:

136.0ms	(pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
45.0ms	(pow (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 3)
192.0ms	(+ (* (pow (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 3) (pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)) (pow 1.0 3))
374.0ms	(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

series5.7s

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)
149.0ms	(pow (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 3)
5.2s	(+ (* (pow (/ (+ alpha beta) (+ (+ alpha beta) (* 2.0 i))) 3) (pow (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3)) (pow 1.0 3))
203.0ms	(- 1.0 (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))

simplify154.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1012	2430
1	4775	2116
2	5001	2116

prune539.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.0b

regimes425.0ms

Accuracy

14.9% (5.4b remaining)

Error of 11.2b against oracle of 5.8b and baseline of 12.2b

bsearch70.0ms

Steps

Iters	Range		Point
8	1.0980023513866943e+148	5.636643246150371e+152	5.508752983092137e+152

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	68
1	54	68

end0.0ms

sample852.0ms

Algorithm

intervals

Results

255.0ms	6376×	body	80	valid
114.0ms	8000×	pre	80	true
101.0ms	509×	body	1280	valid
90.0ms	596×	body	640	valid
38.0ms	321×	body	320	valid
16.0ms	198×	body	160	valid