Details

sample79.0ms

Algorithm

intervals

Results

31.0ms	95×	body	2560	valid
17.0ms	78×	body	1280	valid
8.0ms	283×	body	80	nan
6.0ms	37×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	9×	body	80	valid

simplify95.0ms

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: 0.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- 1.0 (* 5.0 (* v v)))
0.1b	(* 5.0 (* v v))
0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

25.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(- 1.0 (* 5.0 (* v v)))
16.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
60.0ms	(- 1.0 (* 5.0 (* v v)))
25.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	355	664
1	1356	609
2	5001	605

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (* (- (* 5.0 5.0)) (pow v 4)) (* 1.0 1.0)) (+ 1.0 (* 5.0 (* v v))))
0.1b	(* (- (* 5.0 5.0)) (pow v 4))
0.1b	(* 5.0 (* v v))
0.3b	(acos (/ (/ (+ (* (- (* 5.0 5.0)) (pow v 4)) (* 1.0 1.0)) (+ 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
13×	`add-cbrt-cube`
9×	`pow1` `times-frac` `associate-l`
8×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `associate-/l`
2×	`flip3-+` `associate-/r/` `*-commutative` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `distribute-lft-neg-out` `distribute-lft-neg-in` `acos-asin` `pow-to-exp` `neg-mul-1` `distribute-rgt-neg-in` `frac-2neg` `div-exp` `pow-exp` `clear-num` `div-inv`

Counts

4 → 87

Calls

4 calls:

33.0ms	(/ (+ (* (- (* 5.0 5.0)) (pow v 4)) (* 1.0 1.0)) (+ 1.0 (* 5.0 (* v v))))
18.0ms	(* (- (* 5.0 5.0)) (pow v 4))
16.0ms	(* 5.0 (* v v))
2.0ms	(acos (/ (/ (+ (* (- (* 5.0 5.0)) (pow v 4)) (* 1.0 1.0)) (+ 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (+ (* (- (* 5.0 5.0)) (pow v 4)) (* 1.0 1.0)) (+ 1.0 (* 5.0 (* v v))))
37.0ms	(* (- (* 5.0 5.0)) (pow v 4))
31.0ms	(* 5.0 (* v v))
9.0ms	(acos (/ (/ (+ (* (- (* 5.0 5.0)) (pow v 4)) (* 1.0 1.0)) (+ 1.0 (* 5.0 (* v v)))) (- (* v v) 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	420	956
1	2047	850
2	5001	835

prune268.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite21.0ms

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 (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
4.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
12.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
18.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
19.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify110.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	125	1002
1	427	888
2	2342	844
3	5002	813

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.9b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

75×	`sqrt-prod`
63×	`add-sqr-sqrt`
24×	`associate-r` `unswap-sqr`
18×	`unpow-prod-down` `cube-prod`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `associate-l`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`add-log-exp` `sqr-pow`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`acos-asin` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 104

Calls

4 calls:

1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
30.0ms	(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

series47.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
18.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
19.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms	(* (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (pow (sqrt (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) 3))

simplify279.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	209	2416
1	713	1542
2	4762	1477
3	5002	1477

prune196.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes148.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	14
1	30	14
2	31	14
3	31	14

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	3031×	body	2560	valid
555.0ms	2496×	body	1280	valid
227.0ms	8117×	body	80	nan
205.0ms	1249×	body	640	valid
69.0ms	589×	body	320	valid
34.0ms	420×	body	160	valid
11.0ms	215×	body	80	valid