Details

sample40.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
8.0ms	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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.9b

localize14.0ms

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)))

rewrite697.0ms

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:

66.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
180.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
268.0ms	(/ (/ (/ (+ (+ (+ 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))
151.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
29.0ms	(/ (/ (/ (+ (+ (+ 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))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify133.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1513	12983
1	5002	12137

prune4.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite549.0ms

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-r`
40×	`prod-exp`
30×	`1-exp`
29×	`cbrt-undiv`
20×	`associate-/r*`
18×	`associate-l`
15×	`rec-exp`
14×	`unswap-sqr`
12×	`cbrt-unprod` `div-inv`
9×	`distribute-lft-out`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`associate-/l/`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`frac-times` `associate-r/` `associate-l/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 290

Calls

4 calls:

6.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
226.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
153.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
150.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
25.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))
30.0ms	(/ (* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1299	4373
1	5001	3561

prune2.3s

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)))

rewrite5.7s

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:

787.0ms	(/ (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))))))
150.0ms	(/ (+ (+ 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)))))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (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))))))
66.0ms	(/ (+ (+ 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)))))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify12.6s

Algorithm

egg-herbie

Counts

21047 → 21047

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	16693	1402916

prune4.5m

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize34.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.8b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod` `times-frac`
7×	`distribute-lft-out`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow1/3` `associate-/r*`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

144.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
31.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
30.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
32.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series62.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
18.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
16.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	381	1134
1	1443	1047
2	5001	1027

prune3.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes282.0ms

Accuracy

50.4% (1.2b remaining)

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

bsearch22.0ms

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	32	23
1	32	23

end0.0ms

sample972.0ms

Algorithm

intervals

Results

587.0ms	8000×	body	80	valid
233.0ms	8000×	pre	80	true