Details

sample63.0ms

Algorithm

intervals

Results

23.0ms	198×	body	80	valid
8.0ms	24×	body	640	valid
8.0ms	19×	body	1280	valid
7.0ms	256×	pre	80	true
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	107	14
2	479	14
3	2315	14
4	5002	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize13.0ms

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))

1.4b

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

20.1b

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

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
83×	`*-un-lft-identity`
43×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`fma-def`
24×	`associate-/r/`
20×	`distribute-lft-out`
17×	`add-exp-log` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
12×	`div-inv`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
2×	`frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 159

Calls

3 calls:

92.0ms

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

341.0ms

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

27.0ms

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

series578.0ms

Counts

3 → 9

Calls

3 calls:

226.0ms

(/ (/ (* (+ 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)

81.0ms

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

simplify99.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	701	1971
1	3740	1800
2	5001	1782

prune555.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

14.0b

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
162×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
26×	`associate-/l*`
22×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`flip3--` `flip--` `fma-udef`

Counts

3 → 181

Calls

3 calls:

97.0ms

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

22.0ms

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

0.0ms

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series514.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms

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

78.0ms

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

275.0ms

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	727	3112
1	3259	2892
2	5001	2876

prune615.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
14.0b	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
166×	`*-un-lft-identity`
122×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
26×	`associate-/l*`
22×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
12×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `div-sub` `cube-prod` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`cube-mult` `pow-to-exp` `flip3--` `pow-pow` `unpow3` `pow-exp` `flip--` `fma-udef` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 206

Calls

4 calls:

1.0ms	(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
97.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
23.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.3s

Counts

4 → 12

Calls

4 calls:

735.0ms	(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
166.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
74.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
280.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify111.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	823	3541
1	3953	3279
2	5002	3273

prune920.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)) 3)
0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
14.0b	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
172×	`*-un-lft-identity`
128×	`add-sqr-sqrt`
90×	`add-cube-cbrt`
26×	`associate-/l*`
24×	`cbrt-prod`
22×	`distribute-lft-out`
21×	`unpow-prod-down` `cube-prod`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `div-sub` `associate-/l/` `sqr-pow`
2×	`pow-pow` `frac-2neg` `clear-num`
1×	`pow-to-exp` `flip3--` `pow1/3` `pow-exp` `flip--` `fma-udef` `rem-cube-cbrt`

Counts

4 → 231

Calls

4 calls:

6.0ms	(pow (cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)) 3)
97.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
24.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

733.0ms	(pow (cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)) 3)
163.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
270.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify142.0ms

Algorithm

egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	922	4230
1	4441	3836
2	5001	3834

prune833.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

regimes392.0ms

Accuracy

72.3% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 12.3b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	41
1	50	41

end0.0ms

sample1.6s

Algorithm

intervals

Results

653.0ms	6378×	body	80	valid
211.0ms	8000×	pre	80	true
197.0ms	482×	body	1280	valid
197.0ms	609×	body	640	valid
88.0ms	338×	body	320	valid
35.0ms	193×	body	160	valid