Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	19×	body	1280	valid
8.0ms	193×	body	80	valid
5.0ms	256×	pre	80	true
4.0ms	22×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

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: 26.8b

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))

2.1b

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

21.5b

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

rewrite590.0ms

Algorithm

rewrite-expression-head

Rules

4094×	`*-un-lft-identity`
2217×	`distribute-lft-out`
1938×	`times-frac`
816×	`associate-l`
780×	`add-sqr-sqrt`
492×	`add-cube-cbrt`
360×	`associate-r`
141×	`associate-/l*`
72×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
49×	`associate-/l/`
22×	`associate-/r*` `associate-/r/`
18×	`flip3-+` `flip-+`
17×	`add-exp-log` `add-cbrt-cube`
11×	`div-inv`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp`
6×	`flip3--` `flip--`
5×	`add-log-exp`
4×	`associate-r/` `associate-l/`
3×	`pow1` `frac-2neg` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 1221

Calls

3 calls:

77.0ms

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

338.0ms

(+ (/ (/ (* (+ 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)))

series877.0ms

Counts

3 → 9

Calls

3 calls:

254.0ms

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

527.0ms

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

96.0ms

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

simplify266.0ms

Algorithm

egg-herbie

Counts

1230 → 1230

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1424	21651
1	5001	21516

prune930.0ms

Filtered

1230 candidates to 271 candidates (22.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1222	8	1230
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1223	8	1231

Merged error: 6.2b

Counts

1231 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite542.0ms

Algorithm

rewrite-expression-head

Rules

3167×	`*-un-lft-identity`
1611×	`distribute-lft-out`
1394×	`times-frac`
687×	`add-sqr-sqrt`
398×	`associate-l`
374×	`add-cube-cbrt`
334×	`associate-r`
192×	`associate-/l*`
153×	`distribute-lft-out--`
152×	`difference-of-squares`
138×	`frac-times`
94×	`flip3-+` `flip-+`
81×	`associate-/l/`
69×	`associate-*r/`
67×	`associate-/r*`
46×	`associate-/r/`
23×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`clear-num`
9×	`frac-2neg`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
5×	`flip3--` `un-div-inv` `flip--`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`associate-*l/`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 1059

Calls

4 calls:

20.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
41.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
130.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
221.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series830.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
184.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
255.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
299.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify203.0ms

Algorithm

egg-herbie

Counts

1071 → 1071

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1533	14274
1	5002	14147

prune1.1s

Filtered

1071 candidates to 301 candidates (28.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	1064	7	1071
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	1068	11	1079

Merged error: 6.2b

Counts

1079 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.1b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite754.0ms

Algorithm

rewrite-expression-head

Rules

3086×	`*-un-lft-identity`
1579×	`distribute-lft-out`
1359×	`times-frac`
659×	`add-sqr-sqrt`
388×	`associate-l`
362×	`add-cube-cbrt`
334×	`associate-r`
187×	`associate-/l*`
145×	`distribute-lft-out--`
144×	`difference-of-squares`
138×	`frac-times`
93×	`flip3-+` `flip-+`
79×	`associate-/l/`
69×	`associate-*r/`
60×	`associate-/r*`
44×	`associate-/r/`
22×	`div-inv`
19×	`add-exp-log`
18×	`add-cbrt-cube`
10×	`clear-num`
8×	`frac-2neg`
7×	`pow1` `log-pow`
6×	`cbrt-undiv` `exp-prod` `div-exp` `add-log-exp`
5×	`log-prod` `un-div-inv`
4×	`flip3--` `flip--`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`+-commutative` `div-sub` `rem-log-exp` `exp-sum` `associate-*l/`
1×	`pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 1016

Calls

4 calls:

47.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
133.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
228.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
214.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
264.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
323.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
318.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify211.0ms

Algorithm

egg-herbie

Counts

1028 → 1028

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	1560	14077
1	5001	13922

prune1.5s

Filtered

1028 candidates to 284 candidates (27.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	1028	0	1028
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	1028	11	1039

Merged error: 6.2b

Counts

1039 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite848.0ms

Algorithm

rewrite-expression-head

Rules

1675×	`*-un-lft-identity`
845×	`distribute-lft-out`
716×	`times-frac`
372×	`add-sqr-sqrt`
334×	`associate-r`
214×	`associate-l`
203×	`add-cube-cbrt`
141×	`associate-/l*`
138×	`frac-times`
83×	`flip3-+` `flip-+`
81×	`distribute-lft-out--`
80×	`difference-of-squares`
69×	`associate-*r/`
60×	`associate-/l/`
45×	`associate-/r*`
24×	`associate-/r/`
14×	`add-exp-log` `add-cbrt-cube`
12×	`unpow-prod-down` `div-inv`
11×	`cbrt-prod`
8×	`clear-num`
7×	`pow1`
6×	`frac-2neg` `add-log-exp`
5×	`un-div-inv`
4×	`pow-unpow`
3×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `unswap-sqr`
2×	`unpow3` `associate-*l/` `rem-cbrt-cube` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `sum-log` `*-commutative` `rem-cube-cbrt`

Counts

4 → 627

Calls

4 calls:

199.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
195.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
139.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
242.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.6s

Counts

4 → 12

Calls

4 calls:

761.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
286.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
251.0ms	(* (+ 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)

simplify123.0ms

Algorithm

egg-herbie

Counts

639 → 639

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1532	7701
1	5001	7614

prune799.0ms

Filtered

639 candidates to 202 candidates (31.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	634	5	639
Fresh	4	5	9
Picked	1	0	1
Done	0	1	1
Total	639	11	650

Merged error: 6.2b

Counts

650 → 11

regimes240.0ms

Accuracy

3.6% (6.5b remaining)

Error of 12.5b against oracle of 6.0b and baseline of 12.7b

bsearch159.0ms

Steps

Iters	Range		Point
9	3.919704473779381e+257	5.196889498499753e+263	4.159005638992996e+257
3	6.098250721752438e+226	8.407082942025467e+226	7.974176900724274e+226
5	1.1027112679789028e+77	2.926579115410215e+77	2.779043914801437e+77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	65
1	70	65

end0.0ms

sample853.0ms

Algorithm

intervals

Results

253.0ms	6298×	body	80	valid
127.0ms	8000×	pre	80	true
121.0ms	541×	body	1280	valid
103.0ms	608×	body	640	valid
43.0ms	359×	body	320	valid
15.0ms	194×	body	160	valid