Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	210×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	18×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	11×	body	320	valid
0.0ms	6×	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: 21.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b

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

20.1b

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

rewrite468.0ms

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:

91.0ms

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

342.0ms

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

series581.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms

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

272.0ms

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

simplify98.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (78.0ms)

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

prune554.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
0.3b	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b	(/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.3b	(+ (/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite746.0ms

Algorithm

rewrite-expression-head

Rules

2284×	`times-frac`
1863×	`*-un-lft-identity`
1165×	`add-sqr-sqrt`
803×	`add-cube-cbrt`
386×	`fma-def`
349×	`distribute-lft-out`
181×	`distribute-lft-out--` `difference-of-squares`
118×	`associate-/r/`
103×	`associate-/l*`
64×	`div-inv`
55×	`flip3-+` `flip-+`
26×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`div-sub`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `associate-+l-` `flip3--` `sum-log` `flip--`

Counts

4 → 1070

Calls

4 calls:

19.0ms	(/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
5.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
99.0ms	(/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
516.0ms	(+ (/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series541.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
49.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
225.0ms	(/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
184.0ms	(+ (/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify184.0ms

Algorithm

egg-herbie

Counts

1082 → 1082

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1955	13486
1	5001	13315

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b	(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.3b	(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite876.0ms

Algorithm

rewrite-expression-head

Rules

3100×	`times-frac`
2455×	`*-un-lft-identity`
1481×	`add-sqr-sqrt`
1467×	`add-cube-cbrt`
726×	`prod-diff`
493×	`distribute-lft-out`
242×	`fma-neg`
161×	`associate-/r/`
91×	`div-inv`
70×	`flip3-+` `flip-+`
65×	`associate-/l*`
17×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1377

Calls

4 calls:

7.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
5.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
86.0ms	(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
618.0ms	(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series553.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
54.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
164.0ms	(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
285.0ms	(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify370.0ms

Algorithm

egg-herbie

Counts

1389 → 1389

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2598	32465
1	5001	28487

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b	(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.4b	(* (fma i 2.0 (+ alpha beta)) (/ 1 (+ alpha beta)))
1.3b	(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite882.0ms

Algorithm

rewrite-expression-head

Rules

3102×	`times-frac`
2454×	`*-un-lft-identity`
1488×	`add-sqr-sqrt`
1467×	`add-cube-cbrt`
726×	`prod-diff`
492×	`distribute-lft-out`
242×	`fma-neg`
161×	`associate-/r/`
91×	`div-inv`
70×	`flip3-+` `flip-+`
62×	`associate-/l*`
24×	`add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-r`
9×	`div-exp`
8×	`cbrt-undiv` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`associate-l` `unswap-sqr`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rec-exp` `flip3--` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 1385

Calls

4 calls:

5.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
87.0ms	(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms	(* (fma i 2.0 (+ alpha beta)) (/ 1 (+ alpha beta)))
612.0ms	(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series544.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
157.0ms	(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
49.0ms	(* (fma i 2.0 (+ alpha beta)) (/ 1 (+ alpha beta)))
287.0ms	(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify362.0ms

Algorithm

egg-herbie

Counts

1397 → 1397

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	2746	32488
1	5002	28471

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

regimes324.0ms

Accuracy

0% (6.4b remaining)

Error of 11.8b against oracle of 5.4b and baseline of 11.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	32
1	32	32

end0.0ms

sample807.0ms

Algorithm

intervals

Results

252.0ms	6404×	body	80	valid
126.0ms	8000×	pre	80	true
98.0ms	492×	body	1280	valid
86.0ms	551×	body	640	valid
41.0ms	362×	body	320	valid
14.0ms	191×	body	160	valid