Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	200×	body	80	valid
7.0ms	20×	body	1280	valid
6.0ms	22×	body	640	valid
6.0ms	256×	pre	80	true
1.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify49.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ 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)
21.6b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite431.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity` `times-frac`
32×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `associate-/r/` `flip-+`
12×	`distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `div-inv`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`associate-r/` `associate-l` `associate-l/`
3×	`prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

16.0ms	(* (+ alpha beta) (- beta alpha))
90.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
296.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (+ alpha beta) (- beta alpha))
223.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
267.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify114.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	767	2103
1	4353	1976
2	5003	1976

prune419.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

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))
1.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.4b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite392.0ms

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:

21.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
95.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
201.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
54.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series726.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
157.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
220.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
271.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify77.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune762.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
1.3b	(* (+ alpha beta) (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.4b	(+ (* (+ alpha beta) (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

1650×	`times-frac`
1106×	`*-un-lft-identity`
849×	`add-sqr-sqrt`
642×	`add-cube-cbrt`
278×	`associate-r`
138×	`distribute-lft-out`
93×	`distribute-lft-out--` `difference-of-squares`
76×	`associate-/r/`
71×	`associate-/l*`
62×	`add-exp-log`
43×	`div-inv`
35×	`div-exp`
32×	`add-cbrt-cube`
31×	`flip3--` `flip--`
25×	`associate-/r*`
15×	`cbrt-undiv`
8×	`prod-exp`
7×	`pow1`
6×	`rec-exp` `1-exp` `add-log-exp` `unswap-sqr`
5×	`flip3-+` `flip-+`
4×	`associate-l` `cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 800

Calls

4 calls:

111.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
23.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
264.0ms	(* (+ alpha beta) (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
67.0ms	(+ (* (+ alpha beta) (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series750.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
227.0ms	(* (+ alpha beta) (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
284.0ms	(+ (* (+ alpha beta) (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify175.0ms

Algorithm

egg-herbie

Counts

812 → 812

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	2393	14774
1	5002	14103

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

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))
1.3b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.4b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.4b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite561.0ms

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:

93.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
198.0ms	(* (+ 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)
200.0ms	(log (exp (+ (* (+ 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:

165.0ms	(/ (/ (- 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)))
334.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
278.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1073	4732
1	5001	4526

prune830.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

regimes255.0ms

Accuracy

77.9% (1.4b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 12.2b

bsearch3.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	39
1	52	39

end0.0ms

sample1.3s

Algorithm

intervals

Results

479.0ms	6374×	body	80	valid
174.0ms	8000×	pre	80	true
173.0ms	474×	body	1280	valid
169.0ms	605×	body	640	valid
74.0ms	348×	body	320	valid
29.0ms	199×	body	160	valid