Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	43×	body	2560	valid
6.0ms	178×	body	80	valid
4.0ms	26×	body	1280	valid
3.0ms	84×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

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-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

33.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune253.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
4.3b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
24.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
148.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
184.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune485.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
4.3b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
7.5b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
52×	`times-frac`
49×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 138

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
26.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
181.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	696	1715
1	3214	1514
2	5002	1496

prune358.0ms

Filtered

150 candidates to 107 candidates (71.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
11.6b	(/ (* a c) a)
25.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ (* a c) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify36.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	284	413
1	1182	378
2	5001	361

prune166.0ms

Filtered

75 candidates to 55 candidates (73.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

regimes207.0ms

Accuracy

86.5% (3.6b remaining)

Error of 8.9b against oracle of 5.2b and baseline of 32.1b

bsearch141.0ms

Steps

Iters	Range		Point
9	8.465625442272063e+58	8.825425083170634e+65	8.633216037833923e+65
10	-3.103980729665154e-152	-5.819949872588799e-163	-2.630698729571271e-159
8	-183484304836700.72	-121429039431.98735	-73773484249037.31

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	21
1	40	21
2	40	21

end0.0ms

sample1000.0ms

Algorithm

intervals

Results

208.0ms	1040×	body	2560	valid
194.0ms	5929×	body	80	valid
146.0ms	902×	body	1280	valid
92.0ms	2978×	body	80	nan
59.0ms	438×	body	640	valid
28.0ms	108×	body	5120	valid
20.0ms	218×	body	320	valid
7.0ms	104×	body	160	valid