Details

sample314.0ms

Algorithm

intervals

Results

16.0ms	181×	body	80	valid
13.0ms	38×	body	2560	valid
9.0ms	31×	body	1280	valid
5.0ms	66×	body	80	nan
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

32.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune231.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
141.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
169.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune490.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (/ a (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.2b	(/ a (* a c))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`div-exp`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `prod-exp`
9×	`add-cube-cbrt`
8×	`pow1` `cbrt-undiv` `add-log-exp`
6×	`times-frac` `associate-/l*`
5×	`associate-/r/` `cbrt-unprod`
4×	`rec-exp` `flip3--` `1-exp` `sqrt-prod` `flip--`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `diff-log` `associate-r/` `clear-num` `associate-/r` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-*l/` `inv-pow`

Counts

4 → 95

Calls

4 calls:

34.0ms	(/ 1 (* (/ a (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
14.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (* (/ a (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ a (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify61.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	498	912
1	2299	708
2	5001	691

prune206.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.2b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 90

Calls

4 calls:

23.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series319.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ c (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
34.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify150.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	326	944
1	1140	882
2	4781	868
3	5002	868

prune188.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.8b

regimes169.0ms

Accuracy

96.7% (0.8b remaining)

Error of 6.7b against oracle of 5.9b and baseline of 29.9b

bsearch190.0ms

Steps

Iters	Range	Point
10	9.168682727753708e+124	1.4581761209996442e+140	9.792086348653723e+126
10	7.390461352903605e-258	6.899183211307731e-244	7.484772368654571e-258
8	-4.003837004793086e+154	-2.2826144912851317e+150	-1.9721792334777768e+151

Iters

Range

Point

9.168682727753708e+124

1.4581761209996442e+140

9.792086348653723e+126

7.390461352903605e-258

6.899183211307731e-244

7.484772368654571e-258

-4.003837004793086e+154

-2.2826144912851317e+150

-1.9721792334777768e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

436.0ms	5832×	body	80	valid
356.0ms	1078×	body	2560	valid
240.0ms	858×	body	1280	valid
191.0ms	2694×	body	80	nan
106.0ms	461×	body	640	valid
39.0ms	223×	body	320	valid
38.0ms	96×	body	5120	valid
13.0ms	105×	body	160	valid