Details

sample282.0ms

Algorithm

intervals

Results

7.0ms	201×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	21×	body	2560	valid
3.0ms	103×	body	80	nan
2.0ms	3×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
10×	`fma-def` `distribute-lft-out` `add-log-exp`
8×	`distribute-rgt-neg-in`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

47.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune294.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)) a)
1.0b	(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
15×	`times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `fma-def` `sqrt-prod` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`div-sub` `associate-/r*`
2×	`neg-sub0` `associate-+r-` `flip3--` `flip3-+` `sqrt-div` `unsub-neg` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `neg-log` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

43.0ms	(/ (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)) a)
21.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
3.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2)) a)
71.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) (- b_2))
33.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	388	854
1	1480	778
2	5002	756

prune253.0ms

Filtered

112 candidates to 81 candidates (72.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 196

Calls

4 calls:

30.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify83.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	658	2518
1	2948	2155
2	5002	2004

prune328.0ms

Filtered

208 candidates to 104 candidates (50.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (* b_2 b_2) (* a c))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))
19.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
33.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	159	438
1	511	412
2	1701	404
3	5002	394

prune240.0ms

Filtered

78 candidates to 62 candidates (79.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.4b

regimes178.0ms

Accuracy

86.9% (3.7b remaining)

Error of 9.2b against oracle of 5.5b and baseline of 34.1b

bsearch87.0ms

Steps

Iters	Range	Point
2	3.9431530817676045e+109	4.557375181159837e+109	4.019930844191633e+109
10	9.294290849485744e-131	6.48544897696183e-121	1.9238883452280037e-130
3	-2.4188752133425037e+101	-1.756824163423226e+101	-2.377497022722549e+101

Iters

Range

Point

3.9431530817676045e+109

4.557375181159837e+109

4.019930844191633e+109

9.294290849485744e-131

6.48544897696183e-121

1.9238883452280037e-130

-2.4188752133425037e+101

-1.756824163423226e+101

-2.377497022722549e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	41	24
2	41	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

217.0ms	1102×	body	2560	valid
193.0ms	5848×	body	80	valid
143.0ms	920×	body	1280	valid
92.0ms	2883×	body	80	nan
56.0ms	453×	body	640	valid
24.0ms	103×	body	5120	valid
21.0ms	227×	body	320	valid
8.0ms	123×	body	160	valid