Details

sample109.0ms

Algorithm

intervals

Results

42.0ms	92×	body	2560	valid
23.0ms	69×	body	1280	valid
16.0ms	53×	body	640	valid
12.0ms	230×	body	80	nan
3.0ms	18×	body	320	valid
2.0ms	14×	body	160	valid
1.0ms	10×	body	80	valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

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))
0.7b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
4×	`associate-/r*` `difference-of-squares`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l*` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `div-inv` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

9.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series109.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	336	587
1	1261	535
2	5002	531

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* v v) 3)
0.2b	(* (* v v) (* v v))
0.2b	(* 5.0 (* v v))
0.7b	(acos (* (/ (- 1.0 (* 5.0 (* v v))) (- (pow (* v v) 3) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
37×	`pow-prod-up`
27×	`pow-prod-down`
24×	`add-exp-log` `add-cbrt-cube`
23×	`pow-sqr`
19×	`pow-plus`
14×	`pow2`
12×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `pow-pow` `*-un-lft-identity`
4×	`associate-l` `add-log-exp`
3×	`pow-unpow`
2×	`associate-r` `pow-exp` `*-commutative` `rem-cube-cbrt` `unswap-sqr`
1×	`acos-asin` `cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `swap-sqr` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow (* v v) 3)
12.0ms	(* (* v v) (* v v))
6.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ (- 1.0 (* 5.0 (* v v))) (- (pow (* v v) 3) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(pow (* v v) 3)
30.0ms	(* (* v v) (* v v))
28.0ms	(* 5.0 (* v v))
10.0ms	(acos (* (/ (- 1.0 (* 5.0 (* v v))) (- (pow (* v v) 3) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	313	432
1	1243	366
2	5001	366

prune230.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow v 3) (pow v 3))
0.2b	(* (* v v) (* v v))
0.2b	(* 5.0 (* v v))
0.7b	(acos (* (/ (- 1.0 (* 5.0 (* v v))) (- (* (pow v 3) (pow v 3)) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
46×	`add-sqr-sqrt`
37×	`pow-prod-up`
33×	`add-exp-log`
27×	`pow-prod-down`
26×	`unpow-prod-down` `cube-prod`
23×	`pow-sqr` `add-cbrt-cube`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`prod-exp`
19×	`swap-sqr`
18×	`pow-plus` `unswap-sqr`
16×	`associate-l`
14×	`pow2` `associate-r`
12×	`cbrt-unprod` `sqr-pow`
6×	`pow-to-exp` `pow-exp`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`*-commutative`
1×	`acos-asin`

Counts

4 → 170

Calls

4 calls:

11.0ms	(* (pow v 3) (pow v 3))
12.0ms	(* (* v v) (* v v))
10.0ms	(* 5.0 (* v v))
1.0ms	(acos (* (/ (- 1.0 (* 5.0 (* v v))) (- (* (pow v 3) (pow v 3)) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (pow v 3) (pow v 3))
35.0ms	(* (* v v) (* v v))
24.0ms	(* 5.0 (* v v))
9.0ms	(acos (* (/ (- 1.0 (* 5.0 (* v v))) (- (* (pow v 3) (pow v 3)) (pow 1.0 3))) (+ (* (* v v) (* v v)) (+ (* 1.0 1.0) (* (* v v) 1.0)))))

simplify86.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	386	669
1	1824	555
2	5001	531

prune292.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
0.0b	(* 4.0 (+ (pow v 2) (pow v 4)))
0.0b	(+ (pow v 2) (pow v 4))
0.7b	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`associate-r`
3×	`associate-l`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-*r/` `associate--l+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `acos-asin` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

10.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
34.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
9.0ms	(+ (pow v 2) (pow v 4))
0.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series214.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0)
90.0ms	(* 4.0 (+ (pow v 2) (pow v 4)))
70.0ms	(+ (pow v 2) (pow v 4))
5.0ms	(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	222	434
1	995	393
2	5001	386

prune148.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

regimes16.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	2963×	body	2560	valid
821.0ms	2551×	body	1280	valid
421.0ms	7997×	body	80	nan
303.0ms	1255×	body	640	valid
115.0ms	633×	body	320	valid
50.0ms	395×	body	160	valid
15.0ms	203×	body	80	valid