Details

sample34.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	33	17
1	122	15
2	598	13
3	4475	13
4	5001	13

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
587×	`*-un-lft-identity`
341×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 475

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
162.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
240.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
138.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
141.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
71.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify134.0ms

Algorithm

egg-herbie

Counts

487 → 487

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1534	13079
1	5001	12129

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite377.0ms

Algorithm

rewrite-expression-head

Rules

126×	`times-frac`
116×	`*-un-lft-identity`
74×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
21×	`distribute-lft-out`
14×	`associate-/r/`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
9×	`flip3-+` `flip-+` `add-log-exp`
7×	`div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
3×	`frac-2neg` `clear-num` `sum-log` `associate-/l/`
1×	`+-commutative` `associate-+l+` `div-sub` `expm1-udef`

Counts

4 → 186

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
162.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
59.0ms	(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
135.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
144.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
262.0ms	(/ (expm1 (log1p (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify110.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	758	3658
1	3429	3230
2	5002	3202

prune618.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite665.0ms

Algorithm

rewrite-expression-head

Rules

407×	`times-frac`
391×	`*-un-lft-identity`
293×	`sqrt-prod`
222×	`add-sqr-sqrt`
198×	`add-cube-cbrt`
110×	`associate-l`
107×	`distribute-lft-out`
31×	`associate-/r/`
29×	`associate-/l*`
19×	`flip3-+` `flip-+`
16×	`div-inv`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
8×	`sqrt-div` `unswap-sqr`
6×	`pow1` `associate-r`
5×	`associate-/l/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-*r/` `prod-exp` `cbrt-unprod`
1×	`sqrt-undiv` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 389

Calls

4 calls:

236.0ms	(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
134.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
134.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
135.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
193.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

401 → 401

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	995	8715
1	3574	8229
2	5002	8154

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite698.0ms

Algorithm

rewrite-expression-head

Rules

420×	`times-frac`
362×	`*-un-lft-identity`
205×	`sqrt-prod`
199×	`add-sqr-sqrt`
175×	`add-cube-cbrt`
110×	`associate-l`
104×	`distribute-lft-out`
63×	`associate-/l*`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r/`
17×	`div-inv`
12×	`flip3-+` `flip-+`
10×	`sqrt-div`
8×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `associate-r`
5×	`associate-/l/`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-*l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 351

Calls

4 calls:

178.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
237.0ms	(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
121.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
137.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))) (fma 1.0 2.0 (+ alpha beta)))) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
280.0ms	(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify103.0ms

Algorithm

egg-herbie

Counts

363 → 363

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1353	8959
1	5002	8103

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

regimes84.0ms

Accuracy

55.5% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch89.0ms

Steps

Iters	Range		Point
10	2.623187409837306e+205	6.055558237187944e+215	1.1856454375998788e+206

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	36
1	41	36

end0.0ms

sample855.0ms

Algorithm

intervals

Results

576.0ms	8000×	body	80	valid
134.0ms	8000×	pre	80	true