Details

sample82.0ms

Algorithm

intervals

Results

32.0ms	92×	body	2560	valid
21.0ms	80×	body	1280	valid
7.0ms	46×	body	640	valid
7.0ms	245×	body	80	nan
2.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	6×	body	80	valid

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	43	7
2	84	7
3	155	7
4	262	7
5	454	7
6	2878	7
7	5001	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

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))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite16.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `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 → 69

Calls

3 calls:

8.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms	(* 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:

92.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
24.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	349	623
1	1288	567
2	5001	565

prune190.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.0b	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity`
4×	`log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`acos-asin` `log1p-udef` `expm1-log1p` `log1p-expm1` `associate-r` `*-commutative` `expm1-udef` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

1.0ms	(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(expm1 (log1p (acos (/ (- 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)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
132.0ms	(expm1 (log1p (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
30.0ms	(* 5.0 (* v v))
3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify114.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	152	473
1	385	408
2	992	406
3	3312	406
4	5001	406

prune146.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* v v) 3)
0.1b	(* (* v v) (* v v))
0.2b	(* 5.0 (* v v))
0.6b	(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)))))

rewrite25.0ms

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×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `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 → 124

Calls

4 calls:

4.0ms	(pow (* v v) 3)
9.0ms	(* (* v v) (* v v))
6.0ms	(* 5.0 (* v v))
2.0ms	(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)))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (* v v) 3)
31.0ms	(* (* v v) (* v v))
24.0ms	(* 5.0 (* v v))
15.0ms	(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)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	327	490
1	1299	424
2	5002	424

prune268.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* v v) 3)
0.1b	(* (* v v) (* v v))
0.2b	(* 5.0 (* v v))
0.6b	(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)))))

rewrite29.0ms

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×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `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 → 124

Calls

4 calls:

8.0ms	(pow (* v v) 3)
9.0ms	(* (* v v) (* v v))
6.0ms	(* 5.0 (* v v))
2.0ms	(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)))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (* v v) 3)
31.0ms	(* (* v v) (* v v))
24.0ms	(* 5.0 (* v v))
9.0ms	(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)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	327	490
1	1299	424
2	5002	424

prune304.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes106.0ms

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	25	20
1	25	20

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	3068×	body	2560	valid
564.0ms	2476×	body	1280	valid
234.0ms	8249×	body	80	nan
201.0ms	1225×	body	640	valid
73.0ms	605×	body	320	valid
34.0ms	417×	body	160	valid
10.0ms	209×	body	80	valid