Details

sample46.0ms

Algorithm

intervals

Results

15.0ms	197×	body	80	valid
7.0ms	256×	pre	80	true
4.0ms	21×	body	640	valid
4.0ms	14×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify53.0ms

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: 24.3b

localize17.0ms

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))

3.1b

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

17.8b

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

rewrite422.0ms

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:

92.0ms

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

302.0ms

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

24.0ms

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

series569.0ms

Counts

3 → 9

Calls

3 calls:

222.0ms

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

270.0ms

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

77.0ms

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

simplify92.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

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

prune343.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
1.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite390.0ms

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:

96.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
22.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
203.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
52.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series730.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
74.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
227.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
274.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify74.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune778.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
0.3b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
1.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
152×	`*-un-lft-identity`
117×	`add-sqr-sqrt`
90×	`associate-r`
76×	`add-cube-cbrt`
22×	`distribute-lft-out`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `associate-/r/`
10×	`flip3-+` `flip-+`
6×	`pow1` `div-inv` `add-log-exp`
5×	`associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-l`
3×	`unpow-prod-down` `cube-prod` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `frac-times` `cbrt-div` `associate-*l/` `associate-/l/`
1×	`+-commutative` `cube-mult` `flip3--` `frac-2neg` `pow1/3` `unpow3` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--` `rem-cbrt-cube` `sqr-pow`

Counts

4 → 191

Calls

4 calls:

103.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
22.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
203.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
55.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series848.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
73.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
223.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
276.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	970	2869
1	5001	2778

prune630.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
1.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.7b	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
4.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
134×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
90×	`associate-r`
66×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`div-inv`
4×	`log-div` `exp-prod` `associate-l`
3×	`cbrt-undiv` `div-exp` `exp-sum` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `exp-diff` `associate-*l/` `log-pow`
1×	`+-commutative` `associate-r/` `rem-log-exp` `pow-prod-down` `sum-log` `-commutative` `rem-exp-log`

Counts

4 → 159

Calls

4 calls:

54.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
202.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
53.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
53.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

275.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
230.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
271.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
270.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	928	2698
1	5002	2523

prune504.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

regimes287.0ms

Accuracy

13.1% (6.9b remaining)

Error of 11.2b against oracle of 4.2b and baseline of 12.2b

bsearch89.0ms

Steps

Iters	Range		Point
9	1.4193065318071646e+196	6.027709900080744e+203	3.7788486914036184e+202

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

504.0ms	6367×	body	80	valid
210.0ms	8000×	pre	80	true
135.0ms	507×	body	1280	valid
117.0ms	550×	body	640	valid
61.0ms	373×	body	320	valid
28.0ms	203×	body	160	valid