Details

sample86.0ms

Algorithm

intervals

Results

34.0ms	90×	body	2560	valid
23.0ms	83×	body	1280	valid
7.0ms	244×	body	80	nan
6.0ms	34×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	21×	body	160	valid
0.0ms	7×	body	80	valid

simplify125.0ms

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 (0.0%)

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: 0.8b

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))
0.8b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite50.0ms

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:

24.0ms	(/ (- 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)))

series120.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (63.0ms)

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

prune211.0ms

Filtered

202 candidates to 88 candidates (43.6%)

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: 0.8b

Counts

203 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
0.0b	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
0.2b	(* 5.0 (pow v 2))
0.8b	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

365×	`add-sqr-sqrt`
212×	`unpow-prod-down`
160×	`times-frac` `difference-of-squares`
152×	`*-un-lft-identity`
91×	`cbrt-prod`
68×	`unswap-sqr`
52×	`distribute-lft-out--`
47×	`add-cube-cbrt`
40×	`sqr-pow`
38×	`unpow2`
19×	`associate-l`
12×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`associate-r`
7×	`pow1`
4×	`pow-unpow` `associate-/r/` `add-log-exp`
3×	`pow-exp` `prod-exp`
2×	`pow-to-exp` `flip3--` `unpow3` `flip--` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`
1×	`cbrt-undiv` `acos-asin` `pow-pow` `pow1/3` `div-exp` `pow-prod-down` `*-commutative` `cbrt-unprod`

Counts

4 → 241

Calls

4 calls:

24.0ms	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
21.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
6.0ms	(* 5.0 (pow v 2))
1.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))
141.0ms	(pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)
26.0ms	(* 5.0 (pow v 2))
4.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))

simplify118.0ms

Algorithm

egg-herbie

Counts

253 → 253

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1305	3328
1	4036	3096
2	5001	3092

prune372.0ms

Filtered

253 candidates to 117 candidates (46.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	250	3	253
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	253	3	256

Merged error: 0.8b

Counts

256 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 5.0) (sqrt (pow v 2)))
0.8b	(acos (cbrt (* (pow (+ (sqrt 1.0) (* (sqrt 5.0) (sqrt (pow v 2)))) 3) (pow (/ (- (sqrt 1.0) (* (sqrt 5.0) (sqrt (pow v 2)))) (- (pow v 2) 1.0)) 3))))
27.2b	(sqrt (pow v 2))
27.2b	(sqrt (pow v 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`sqrt-prod`
35×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`sqrt-pow1`
13×	`unpow-prod-down`
12×	`pow1`
11×	`associate-r`
10×	`unswap-sqr`
8×	`rem-sqrt-square`
7×	`unpow2` `sqr-pow`
6×	`add-exp-log` `pow-unpow` `associate-l` `add-cbrt-cube`
4×	`pow1/2` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-pow`
1×	`acos-asin` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 101

Calls

4 calls:

9.0ms	(* (sqrt 5.0) (sqrt (pow v 2)))
1.0ms	(acos (cbrt (* (pow (+ (sqrt 1.0) (* (sqrt 5.0) (sqrt (pow v 2)))) 3) (pow (/ (- (sqrt 1.0) (* (sqrt 5.0) (sqrt (pow v 2)))) (- (pow v 2) 1.0)) 3))))
5.0ms	(sqrt (pow v 2))
3.0ms	(sqrt (pow v 2))

series80.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sqrt 5.0) (sqrt (pow v 2)))
21.0ms	(acos (cbrt (* (pow (+ (sqrt 1.0) (* (sqrt 5.0) (sqrt (pow v 2)))) 3) (pow (/ (- (sqrt 1.0) (* (sqrt 5.0) (sqrt (pow v 2)))) (- (pow v 2) 1.0)) 3))))
9.0ms	(sqrt (pow v 2))
9.0ms	(sqrt (pow v 2))

simplify138.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	206	657
1	674	569
2	3126	565
3	5002	563

prune389.0ms

Filtered

113 candidates to 80 candidates (70.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Merged error: 0.8b

Counts

116 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))
0.9b	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
0.9b	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
1.0b	(* (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))) (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))
1.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
1.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
6.0ms	(* (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))) (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))
18.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
18.0ms	(sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3))))
5.0ms	(* (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))) (sqrt (acos (cbrt (pow (/ (- 1.0 (* 5.0 (pow v 2))) (- (pow v 2) 1.0)) 3)))))

simplify145.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	120	1162
1	434	989
2	2413	932
3	5001	893

prune179.0ms

Filtered

95 candidates to 56 candidates (58.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	93	6	99

Merged error: 0.8b

Counts

99 → 6

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	20
1	22	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	2949×	body	2560	valid
601.0ms	2510×	body	1280	valid
217.0ms	7861×	body	80	nan
203.0ms	1224×	body	640	valid
78.0ms	642×	body	320	valid
39.0ms	472×	body	160	valid
10.0ms	203×	body	80	valid