Details

sample81.0ms

Algorithm

intervals

Results

33.0ms	96×	body	2560	valid
19.0ms	82×	body	1280	valid
7.0ms	265×	body	80	nan
6.0ms	35×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	7×	body	80	valid

simplify104.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

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))
0.5b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite20.0ms

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:

11.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series122.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
31.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

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

prune183.0ms

Filtered

78 candidates to 61 candidates (78.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.2b	(* 5.0 (* v v))
0.6b	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

65×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
49×	`times-frac`
39×	`prod-diff`
13×	`fma-neg`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`add-log-exp` `difference-of-squares`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*`
2×	`asin-acos` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 139

Calls

4 calls:

13.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
15.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
7.0ms	(* 5.0 (* v v))
1.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
38.0ms	(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
27.0ms	(* 5.0 (* v v))
4.0ms	(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify74.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	576	2948
1	1941	1851
2	5003	1839

prune334.0ms

Filtered

151 candidates to 97 candidates (64.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
0.2b	(* 5.0 (* v v))
2.1b	(asin (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`times-frac`
34×	`add-cube-cbrt`
33×	`add-exp-log`
25×	`associate-r`
23×	`add-cbrt-cube`
21×	`associate-l`
14×	`difference-of-squares`
11×	`pow1` `prod-exp`
9×	`div-exp`
7×	`sqrt-prod` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `div-inv` `distribute-lft-out` `associate-/l*`
2×	`rec-exp` `1-exp` `*-commutative` `associate-/l/`
1×	`frac-times` `asin-acos` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `associate-l/` `clear-num` `flip-+`

Counts

4 → 151

Calls

4 calls:

45.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
16.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
7.0ms	(* 5.0 (* v v))
1.0ms	(asin (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0))))
98.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))
29.0ms	(* 5.0 (* v v))
12.0ms	(asin (* (/ 1 (+ v (sqrt 1.0))) (/ (- 1.0 (* 5.0 (* v v))) (- v (sqrt 1.0)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	805	1872
1	3924	1600
2	5001	1563

prune439.0ms

Filtered

163 candidates to 111 candidates (68.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

1.0ms	(sqrt PI)
0.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)

simplify59.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	86	251
1	161	234
2	353	168
3	1306	159
4	5002	156

prune191.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.5b

regimes67.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	9
1	14	9

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2937×	body	2560	valid
603.0ms	2559×	body	1280	valid
207.0ms	7763×	body	80	nan
203.0ms	1239×	body	640	valid
73.0ms	629×	body	320	valid
34.0ms	419×	body	160	valid
11.0ms	217×	body	80	valid