Details

sample35.0ms

Algorithm

intervals

Results

19.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify83.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.4b

Counts

2 → 1

localize12.0ms

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))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite107.0ms

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:

7.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
35.0ms	(/ (/ (/ (+ (+ (+ 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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (/ (+ (+ (+ 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))
17.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm

egg-herbie

Counts

477 → 477

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1492	13034
1	5002	12552

prune1.3s

Filtered

477 candidates to 281 candidates (41.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	470	7	477
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	471	7	478

Merged error: 1.6b

Counts

478 → 7

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 3.0)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite121.0ms

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*`
62×	`associate-/r/`
33×	`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` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 524

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
18.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
20.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
22.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify153.0ms

Algorithm

egg-herbie

Counts

536 → 536

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1527	13829
1	5001	13288

prune1.1s

Filtered

536 candidates to 279 candidates (47.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	533	3	536
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	536	7	543

Merged error: 1.6b

Counts

543 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ (* (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

1423×	`times-frac`
987×	`*-un-lft-identity`
648×	`add-sqr-sqrt`
555×	`add-cube-cbrt`
534×	`associate-r`
444×	`cbrt-prod`
272×	`sqrt-prod`
216×	`distribute-lft-out`
66×	`associate-/r/`
46×	`add-exp-log`
37×	`add-cbrt-cube`
36×	`flip3-+` `flip-+`
33×	`div-inv`
24×	`unswap-sqr`
18×	`cbrt-undiv` `div-exp`
12×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
10×	`sqrt-div`
9×	`associate-/r*`
6×	`pow1` `associate-/l/`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 705

Calls

4 calls:

213.0ms	(* (/ (* (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ 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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (/ (* (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (cbrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
19.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify285.0ms

Algorithm

egg-herbie

Counts

717 → 717

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	3147	29800
1	5001	28964

prune3.8s

Filtered

717 candidates to 343 candidates (52.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	717	0	717
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	717	7	724

Merged error: 1.6b

Counts

724 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
0.1b	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
4.3b	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

2007×	`times-frac`
1747×	`*-un-lft-identity`
798×	`cbrt-prod`
789×	`add-sqr-sqrt` `add-cube-cbrt`
550×	`distribute-lft-out`
360×	`unpow-prod-down` `cube-prod`
145×	`associate-/l*`
96×	`associate-/r/`
49×	`flip3-+` `flip-+`
48×	`div-inv`
20×	`cube-mult` `unpow3` `sqr-pow`
14×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`associate-/r*`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/l/`
2×	`cube-div` `frac-2neg` `pow-exp` `clear-num` `rem-cube-cbrt`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `rem-cbrt-cube`

Counts

4 → 1011

Calls

4 calls:

53.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
16.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))

series84.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (/ (cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ beta 3.0)))
38.0ms	(pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3)
12.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
12.0ms	(cbrt (pow (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) 3))

simplify295.0ms

Algorithm

egg-herbie

Counts

1023 → 1023

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	2002	28666
1	5002	28279

prune1.8s

Filtered

1023 candidates to 327 candidates (68.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1022	1	1023
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	1023	7	1030

Merged error: 1.6b

Counts

1030 → 7

regimes110.0ms

Accuracy

52.8% (1.3b remaining)

Error of 2.6b against oracle of 1.3b and baseline of 4.0b

bsearch16.0ms

Steps

Iters	Range		Point
6	1.0707519652442772e+126	4.723892664260672e+126	4.6781406697324435e+126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	30
1	45	30

end0.0ms

sample846.0ms

Algorithm

intervals

Results

495.0ms	8000×	body	80	valid
139.0ms	8000×	pre	80	true

Details

sample35.0ms

simplify83.0ms

prune3.0ms

localize12.0ms

rewrite107.0ms

series63.0ms

simplify140.0ms

prune1.3s

localize13.0ms

rewrite121.0ms

series59.0ms

simplify153.0ms

prune1.1s

localize18.0ms

rewrite330.0ms

series67.0ms

simplify285.0ms

prune3.8s

localize16.0ms

rewrite204.0ms

series84.0ms

simplify295.0ms

prune1.8s

regimes110.0ms

bsearch16.0ms

simplify2.0ms

end0.0ms

sample846.0ms

Profiling