Details

sample22.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify77.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize11.0ms

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))
1.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite684.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`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` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

66.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
175.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
259.0ms	(/ (/ (/ (+ (+ (+ 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))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
137.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
146.0ms	(/ (/ (/ (+ (+ (+ 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))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify137.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune949.0ms

Filtered

477 candidates to 281 candidates (58.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize13.0ms

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)))
1.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite612.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
66×	`associate-/r/`
37×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `frac-add` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 528

Calls

4 calls:

13.0ms	(+ (+ alpha beta) (* beta alpha))
176.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
231.0ms	(/ (/ (/ (+ (+ (+ 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)))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
144.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (/ (/ (+ (+ (+ 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)))

simplify159.0ms

Algorithm

egg-herbie

Counts

540 → 540

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1632	15099
1	5001	14543

prune1.0s

Filtered

540 candidates to 284 candidates (52.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.1b	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
1.7b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite748.0ms

Algorithm

rewrite-expression-head

Rules

4248×	`times-frac`
2962×	`*-un-lft-identity`
1614×	`add-sqr-sqrt` `add-cube-cbrt`
766×	`distribute-lft-out`
248×	`associate-/l*`
185×	`associate-/r/`
102×	`div-inv`
84×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
30×	`associate-/r*`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`frac-2neg` `frac-add` `clear-num` `associate-/l/` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1525

Calls

4 calls:

153.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
87.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
236.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
97.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series469.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
79.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
157.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
94.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify474.0ms

Algorithm

egg-herbie

Counts

1537 → 1537

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3967	49351
1	5001	47922

prune2.9s

Filtered

1537 candidates to 700 candidates (45.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
0.1b	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
14.4b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite441.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
109×	`add-sqr-sqrt` `*-un-lft-identity`
96×	`add-cube-cbrt`
54×	`add-exp-log`
51×	`associate-r`
34×	`add-cbrt-cube`
26×	`div-exp` `associate-/r/`
19×	`flip3-+` `flip-+` `associate-/l*`
14×	`cbrt-undiv`
12×	`div-inv`
11×	`associate-/r*`
10×	`pow1` `prod-exp`
7×	`distribute-lft-out`
6×	`cbrt-unprod` `associate-/l/`
5×	`unswap-sqr`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `frac-add` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `associate-*r/` `inv-pow` `pow-div`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 241

Calls

4 calls:

17.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
122.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
44.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
246.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
151.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
58.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
143.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify58.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1091	4009
1	5002	3468

prune626.0ms

Filtered

253 candidates to 175 candidates (69.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes66.0ms

Accuracy

68% (1.3b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 4.1b

bsearch88.0ms

Steps

Iters	Range		Point
11	7.8512521379903e+159	1.3123977658214608e+188	8.012177184264198e+159

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	31
1	42	31

end0.0ms

sample531.0ms

Algorithm

intervals

Results

291.0ms	8000×	body	80	valid
91.0ms	8000×	pre	80	true