Details

sample35.0ms

Algorithm

intervals

Results

8.0ms	205×	body	80	valid
7.0ms	19×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	15×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify54.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.0b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.1b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* 2.0 i))
91.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
340.0ms	(+ (/ (/ (* (+ 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)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* 2.0 i))
232.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
274.0ms	(+ (/ (/ (* (+ 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)))

simplify109.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	724	2051
1	4101	1860
2	5001	1852

prune609.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
0.5b	(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
3.4b	(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

12400×	`times-frac`
9469×	`*-un-lft-identity`
5477×	`add-sqr-sqrt`
4067×	`add-cube-cbrt`
1996×	`distribute-lft-out`
1418×	`fma-def`
705×	`distribute-lft-out--` `difference-of-squares`
400×	`associate-/r/`
378×	`associate-/l*`
205×	`div-inv`
164×	`flip3-+` `flip-+`
125×	`associate-/r*`
62×	`add-exp-log`
43×	`div-exp`
32×	`flip3--` `add-cbrt-cube` `flip--`
19×	`cbrt-undiv`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

4 → 3880

Calls

4 calls:

184.0ms	(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
25.0ms	(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
35.0ms	(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
1.2s	(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series615.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
66.0ms	(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
140.0ms	(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
125.0ms	(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify544.0ms

Algorithm

egg-herbie

Counts

3892 → 3892

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5001	55520

prune9.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (fma 2.0 i beta) alpha) (+ alpha beta))
0.1b	(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
0.5b	(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
11.8b	(fma (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

1330×	`times-frac`
1138×	`*-un-lft-identity`
702×	`add-sqr-sqrt`
480×	`add-cube-cbrt`
218×	`distribute-lft-out`
125×	`associate-/r*`
111×	`distribute-lft-out--` `difference-of-squares`
65×	`associate-/r/`
33×	`div-inv`
32×	`add-exp-log`
29×	`associate-/l*`
28×	`flip3-+` `flip-+`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `fma-udef` `inv-pow`

Counts

4 → 702

Calls

4 calls:

11.0ms	(/ (+ (fma 2.0 i beta) alpha) (+ alpha beta))
22.0ms	(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
39.0ms	(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
0.0ms	(fma (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series344.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (+ (fma 2.0 i beta) alpha) (+ alpha beta))
63.0ms	(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
146.0ms	(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
82.0ms	(fma (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify126.0ms

Algorithm

egg-herbie

Counts

714 → 714

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1681	10095
1	5001	9342

prune1.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.8b	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
410×	`*-un-lft-identity`
284×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
156×	`sqrt-prod`
63×	`distribute-lft-out`
42×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
19×	`div-inv`
18×	`add-exp-log`
17×	`associate-/r*`
16×	`add-cbrt-cube`
11×	`flip3-+` `flip-+`
9×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`flip3--` `1-exp` `flip--` `fma-udef`

Counts

4 → 402

Calls

4 calls:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
98.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
76.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series651.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
214.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
135.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
229.0ms	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1283	7520
1	5002	6956

prune968.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

regimes284.0ms

Accuracy

11.5% (5.9b remaining)

Error of 11.6b against oracle of 5.8b and baseline of 12.4b

bsearch82.0ms

Steps

Iters	Range		Point
9	5.5711449815597784e+107	2.322222932224586e+113	2.2383019899999203e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample807.0ms

Algorithm

intervals

Results

254.0ms	6372×	body	80	valid
128.0ms	8000×	pre	80	true
101.0ms	495×	body	1280	valid
89.0ms	567×	body	640	valid
42.0ms	363×	body	320	valid
16.0ms	203×	body	160	valid