Details

sample57.0ms

Algorithm

intervals

Results

20.0ms	206×	body	80	valid
7.0ms	14×	body	640	valid
7.0ms	256×	pre	80	true
5.0ms	18×	body	320	valid
4.0ms	10×	body	1280	valid
1.0ms	8×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

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))

3.0b

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

20.8b

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

rewrite444.0ms

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:

97.0ms

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

316.0ms

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

series588.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms

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

278.0ms

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

80.0ms

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

simplify91.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (17.0ms)

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

prune365.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

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))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.7b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite414.0ms

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:

23.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
100.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
213.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
58.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series740.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
161.0ms	(/ (/ (- 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)))
277.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605

prune806.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.2b	(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.7b	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 155

Calls

4 calls:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
56.0ms	(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
171.0ms	(* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
98.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series663.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
80.0ms	(* (+ 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)))
277.0ms	(+ (* (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify122.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	855	2016
1	4821	1785
2	5002	1784

prune457.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.7b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.8b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite598.0ms

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:

100.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
212.0ms	(* (+ 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)
212.0ms	(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:

159.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
373.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
278.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
289.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1073	4732
1	5001	4526

prune826.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

regimes213.0ms

Accuracy

-9% (7.1b remaining)

Error of 13.2b against oracle of 6.1b and baseline of 12.6b

bsearch51.0ms

Steps

Iters	Range		Point
5	2.575085000628985e+91	6.345546729328193e+91	2.6098868310212144e+91
0	8.598091656039184e+36	8.822923466294868e+36	8.710507561167026e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	27
1	54	27

end0.0ms

sample1.6s

Algorithm

intervals

Results

636.0ms	6320×	body	80	valid
201.0ms	501×	body	1280	valid
198.0ms	8000×	pre	80	true
193.0ms	578×	body	640	valid
101.0ms	397×	body	320	valid
36.0ms	204×	body	160	valid