Details

sample33.0ms

Algorithm

intervals

Results

8.0ms	213×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	13×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	6×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize16.0ms

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)

19.6b

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

rewrite426.0ms

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:

94.0ms

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

304.0ms

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

series604.0ms

Counts

3 → 9

Calls

3 calls:

238.0ms

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

284.0ms

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

82.0ms

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

simplify95.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

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

prune366.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

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))
3.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite396.0ms

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:

22.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
97.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
207.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
53.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series775.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
171.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
239.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
286.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify70.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune856.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.2b

localize16.0ms

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))) 3)
3.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b	(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
13.9b	(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
135×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
90×	`associate-r`
65×	`add-cube-cbrt`
23×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
12×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
10×	`cube-div` `associate-/r/`
9×	`pow1`
8×	`cbrt-prod`
6×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`cbrt-div` `div-inv`
4×	`associate-l` `pow-exp` `rem-cube-cbrt`
3×	`pow-unpow` `associate-*r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow1/3` `sum-log` `*-commutative` `rem-cbrt-cube`

Counts

4 → 182

Calls

4 calls:

55.0ms	(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
206.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
9.0ms	(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
2.0ms	(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

series3.4s

Counts

4 → 12

Calls

4 calls:

2.7s	(pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)
233.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
287.0ms	(+ (cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3)) 1.0)
233.0ms	(cbrt (pow (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	998	2759
1	5001	2613

prune798.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
3.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.2b	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
3.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite378.0ms

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:

55.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
205.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
55.0ms	(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)

series1.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
238.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
279.0ms	(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))
285.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	931	2698
1	5001	2523

prune517.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.8b

regimes305.0ms

Accuracy

54.7% (3.8b remaining)

Error of 7.8b against oracle of 4.0b and baseline of 12.4b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	39
1	52	39

end0.0ms

sample837.0ms

Algorithm

intervals

Results

260.0ms	6353×	body	80	valid
127.0ms	8000×	pre	80	true
107.0ms	511×	body	1280	valid
90.0ms	572×	body	640	valid
44.0ms	375×	body	320	valid
15.0ms	189×	body	160	valid