Details

sample88.0ms

Algorithm

intervals

Results

35.0ms	86×	body	2560	valid
22.0ms	88×	body	1280	valid
8.0ms	244×	body	80	nan
7.0ms	40×	body	640	valid
2.0ms	19×	body	320	valid
2.0ms	18×	body	160	valid
0.0ms	5×	body	80	valid

simplify121.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2776	7
7	5002	7

prune2.0ms

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: 0.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

351×	`add-sqr-sqrt`
126×	`difference-of-squares`
124×	`*-un-lft-identity`
110×	`times-frac`
85×	`unswap-sqr`
46×	`distribute-lft-out--`
32×	`add-cube-cbrt`
29×	`associate-l`
27×	`swap-sqr`
26×	`*-commutative`
18×	`associate-r`
11×	`associate-/l*`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`pow1`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 193

Calls

3 calls:

27.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series127.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms	(* 5.0 (* v v))
9.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify87.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	577	2078
1	2023	2022
2	5001	2008

prune221.0ms

Filtered

202 candidates to 88 candidates (56.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	3	203

Merged error: 0.3b

Counts

203 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

1375×	`add-sqr-sqrt`
788×	`times-frac`
565×	`*-un-lft-identity`
471×	`difference-of-squares`
298×	`unswap-sqr`
216×	`add-cube-cbrt`
174×	`distribute-lft-out--`
127×	`associate-/r*`
93×	`associate-l`
90×	`swap-sqr`
89×	`*-commutative`
34×	`associate-/r/`
19×	`add-exp-log`
18×	`associate-r`
16×	`associate-/l*`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp`
5×	`flip3--` `flip--` `div-inv`
4×	`remove-double-div`
3×	`cbrt-undiv` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-/l/`
1×	`acos-asin` `pow-flip` `inv-pow`

Counts

3 → 562

Calls

3 calls:

50.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
10.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

series131.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
28.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

simplify125.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1282	7535
1	5002	6902

prune487.0ms

Filtered

571 candidates to 171 candidates (70.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	567	4	571
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	570	4	574

Merged error: 0.3b

Counts

574 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
0.0b	(exp (log (acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))))
0.2b	(* 5.0 (* v v))
0.3b	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

1378×	`add-sqr-sqrt`
788×	`times-frac`
568×	`*-un-lft-identity`
471×	`difference-of-squares`
298×	`unswap-sqr`
219×	`add-cube-cbrt`
174×	`distribute-lft-out--`
127×	`associate-/r*`
93×	`associate-l`
90×	`swap-sqr`
89×	`*-commutative`
34×	`associate-/r/`
20×	`add-exp-log`
18×	`associate-r`
16×	`associate-/l*`
14×	`add-cbrt-cube`
11×	`pow1`
7×	`div-exp`
5×	`flip3--` `flip--` `div-inv` `add-log-exp`
4×	`exp-prod` `remove-double-div`
3×	`cbrt-undiv` `log-prod` `exp-sum` `pow-prod-down` `prod-exp` `clear-num` `cbrt-unprod`
2×	`rec-exp` `frac-2neg` `1-exp` `rem-exp-log` `associate-/l/`
1×	`acos-asin` `pow-flip` `log-pow` `inv-pow`

Counts

4 → 578

Calls

4 calls:

50.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
2.0ms	(exp (log (acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))))
10.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v)))))
4.0ms	(exp (log (acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))))
26.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ 1 (/ (- (* v v) 1.0) (- 1.0 (* 5.0 (* v v))))))

simplify130.0ms

Algorithm

egg-herbie

Counts

590 → 590

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1310	7733
1	5001	7082

prune614.0ms

Filtered

590 candidates to 181 candidates (69.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	588	2	590
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	591	3	594

Merged error: 0.3b

Counts

594 → 3

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 5.0 (* v v))
0.2b	(* 5.0 (* v v))
1.6b	(acos (/ (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ (sqrt 1.0) (fabs v))) (/ (- (sqrt (* v v)) (sqrt 1.0)) (sqrt (- 1.0 (* 5.0 (* v v)))))))
27.2b	(sqrt (* v v))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
39×	`associate-r`
22×	`pow1`
21×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`associate-l` `sqrt-prod`
14×	`add-exp-log` `add-cbrt-cube`
12×	`swap-sqr`
8×	`*-commutative`
7×	`pow-prod-down`
6×	`sqrt-pow1` `prod-exp` `cbrt-unprod`
5×	`rem-sqrt-square`
4×	`add-log-exp`
1×	`pow2` `acos-asin` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 116

Calls

4 calls:

10.0ms	(* 5.0 (* v v))
10.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ (sqrt 1.0) (fabs v))) (/ (- (sqrt (* v v)) (sqrt 1.0)) (sqrt (- 1.0 (* 5.0 (* v v)))))))
5.0ms	(sqrt (* v v))

series82.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 5.0 (* v v))
31.0ms	(* 5.0 (* v v))
13.0ms	(acos (/ (/ (sqrt (- 1.0 (* 5.0 (* v v)))) (+ (sqrt 1.0) (fabs v))) (/ (- (sqrt (* v v)) (sqrt 1.0)) (sqrt (- 1.0 (* 5.0 (* v v)))))))
10.0ms	(sqrt (* v v))

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	260	587
1	1054	511
2	5001	505

prune340.0ms

Filtered

128 candidates to 74 candidates (42.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	128	3	131

Merged error: 0.3b

Counts

131 → 3

regimes50.0ms

Accuracy

0% (0.5b remaining)

Error of 1.1b against oracle of 0.6b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	21
1	20	21

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	2919×	body	2560	valid
652.0ms	2465×	body	1280	valid
249.0ms	1324×	body	640	valid
235.0ms	7957×	body	80	nan
82.0ms	614×	body	320	valid
45.0ms	456×	body	160	valid
12.0ms	222×	body	80	valid