Details

sample32.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	24×	body	640	valid
3.0ms	16×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	5×	body	160	valid

simplify51.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 24.1b

Counts

2 → 1

localize13.0ms

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))

2.3b

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

19.7b

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

rewrite71.0ms

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:

20.0ms

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

33.0ms

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

13.0ms

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

series572.0ms

Counts

3 → 9

Calls

3 calls:

225.0ms

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

269.0ms

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

78.0ms

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

simplify94.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (18.0ms)

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

prune342.0ms

Filtered

120 candidates to 89 candidates (74.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	9	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Merged error: 5.7b

Counts

121 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.8b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite119.0ms

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:

9.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
41.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series742.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
165.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
226.0ms	(* (+ 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)

simplify80.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune786.0ms

Filtered

307 candidates to 199 candidates (64.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	301	6	307
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	306	10	316

Merged error: 5.7b

Counts

316 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.9b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.8b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.8b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
274×	`*-un-lft-identity`
195×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
11×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`log-prod` `associate-l` `associate-/r*` `log-pow`
3×	`exp-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `div-sub` `associate-*l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `associate-/l/`

Counts

4 → 271

Calls

4 calls:

20.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
42.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
27.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series945.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
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)
285.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1076	4732
1	5001	4526

prune850.0ms

Filtered

283 candidates to 184 candidates (65.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	283	10	293

Merged error: 5.7b

Counts

293 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b	(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.8b	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
52×	`add-exp-log`
42×	`add-sqr-sqrt`
40×	`times-frac`
39×	`associate-r`
32×	`add-cbrt-cube`
31×	`add-cube-cbrt`
22×	`prod-exp`
13×	`div-exp`
12×	`pow1` `cbrt-unprod`
11×	`frac-times` `associate-*l/`
10×	`flip3-+` `flip-+`
8×	`distribute-lft-out`
7×	`cbrt-undiv`
6×	`associate-/r/` `add-log-exp`
5×	`associate-l`
4×	`rec-exp` `1-exp` `associate-r/` `pow-prod-down` `associate-/r`
3×	`div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `unswap-sqr`
1×	`+-commutative` `pow-flip` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `inv-pow`

Counts

4 → 152

Calls

4 calls:

9.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
26.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
27.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series686.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
98.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
226.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
285.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify113.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	811	1947
1	4626	1704
2	5002	1669

prune362.0ms

Filtered

164 candidates to 99 candidates (60.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	163	11	174

Merged error: 5.7b

Counts

174 → 11

regimes228.0ms

Accuracy

4.2% (6.0b remaining)

Error of 12.0b against oracle of 6.0b and baseline of 12.3b

bsearch65.0ms

Steps

Iters	Range		Point
9	1.2170053709950026e+64	2.6208157583297256e+69	2.5910419616899343e+69

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	27
1	48	27

end0.0ms

sample828.0ms

Algorithm

intervals

Results

252.0ms	6370×	body	80	valid
128.0ms	8000×	pre	80	true
109.0ms	527×	body	1280	valid
81.0ms	513×	body	640	valid
45.0ms	381×	body	320	valid
17.0ms	209×	body	160	valid