Details

sample22.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify82.0ms

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite667.0ms

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`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`fma-def` `frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 476

Calls

4 calls:

63.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
172.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
256.0ms	(/ (/ (/ (+ (+ (+ 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))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
142.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms	(/ (/ (/ (+ (+ (+ 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))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify138.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.1b	(* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
0.1b	(/ (* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

196×	`times-frac`
167×	`add-exp-log`
145×	`add-sqr-sqrt`
128×	`*-un-lft-identity`
102×	`div-exp`
100×	`add-cube-cbrt`
61×	`add-cbrt-cube`
44×	`associate-l`
40×	`prod-exp`
30×	`1-exp`
29×	`cbrt-undiv`
20×	`associate-/r*`
16×	`associate-r`
15×	`rec-exp`
14×	`unswap-sqr`
12×	`cbrt-unprod` `div-inv`
9×	`distribute-lft-out`
8×	`associate-/l*`
7×	`pow1`
5×	`associate-/l/`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `flip-+`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 284

Calls

4 calls:

5.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
168.0ms	(* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
137.0ms	(/ (* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
150.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
145.0ms	(* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
156.0ms	(/ (* (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify69.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1190	4080
1	5001	3500

prune639.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite5.9s

Algorithm

rewrite-expression-head

Rules

98889×	`times-frac`
64792×	`*-un-lft-identity`
38820×	`sqrt-prod`
32650×	`add-sqr-sqrt` `add-cube-cbrt`
18119×	`distribute-lft-out`
5246×	`associate-/r/`
2656×	`div-inv`
2593×	`flip3-+` `flip-+`
389×	`associate-/r*`
76×	`associate-/l*`
66×	`sqrt-div`
15×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

4 → 21035

Calls

4 calls:

902.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
144.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
145.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
274.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
75.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
78.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify12.5s

Algorithm

egg-herbie

Counts

21047 → 21047

Iterations

Useful iterations: 0 (173.0ms)

Iter	Nodes	Cost
0	16693	1402916

prune1.0m

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
0.1b	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.6b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite17.4s

Algorithm

rewrite-expression-head

Rules

346941×	`times-frac`
207961×	`*-un-lft-identity`
115203×	`sqrt-prod`
114448×	`add-sqr-sqrt` `add-cube-cbrt`
52679×	`distribute-lft-out`
15104×	`associate-/r/`
8128×	`div-inv`
6979×	`flip3-+` `flip-+`
390×	`associate-/r*`
198×	`associate-/l*`
189×	`sqrt-div`
15×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60518

Calls

4 calls:

1.6s	(/ (sqrt (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
144.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
92.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (sqrt (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
274.0ms	(/ (+ (+ alpha beta) (fma 2.0 1.0 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
86.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
79.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify41.0s

Algorithm

egg-herbie

Counts

60530 → 60530

Iterations

Useful iterations: 0 (767.0ms)

Iter	Nodes	Cost
0	47443	4331251

prune3.2m

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes84.0ms

Accuracy

50.3% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch65.0ms

Steps

Iters	Range		Point
8	1.9245522684738998e+169	2.4018236880003466e+173	1.7018668465525539e+171

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	35
1	38	35
2	38	35

end0.0ms

sample481.0ms

Algorithm

intervals

Results

270.0ms	8000×	body	80	valid
81.0ms	8000×	pre	80	true

Details

sample22.0ms

simplify82.0ms

prune7.0ms

localize15.0ms

rewrite667.0ms

series386.0ms

simplify138.0ms

prune1.1s

localize15.0ms

rewrite475.0ms

series421.0ms

simplify69.0ms

prune639.0ms

localize16.0ms

rewrite5.9s

series582.0ms

simplify12.5s

prune1.0m

localize20.0ms

rewrite17.4s

series597.0ms

simplify41.0s

prune3.2m

regimes84.0ms

bsearch65.0ms

simplify2.0ms

end0.0ms

sample481.0ms

end4.4m