Details

sample277.0ms

Algorithm

intervals

Results

6.0ms	35×	body	2560	valid
6.0ms	33×	body	1280	valid
6.0ms	181×	body	80	valid
3.0ms	92×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	2×	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: 37.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.0b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

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:

10.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

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

prune245.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

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:

8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(/ (/ (+ 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)))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (87.0ms)

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

prune523.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
58×	`times-frac`
35×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`associate-l`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`distribute-rgt-neg-in` `prod-exp` `add-log-exp`
7×	`pow1` `associate-/r*`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 151

Calls

4 calls:

8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
16.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
173.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	711	2040
1	3338	1826
2	5001	1813

prune405.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.1b	(/ (* a c) a)
23.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(/ (* a c) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series171.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ (* a c) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify38.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	301	458
1	1316	420
2	5002	400

prune185.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes185.0ms

Accuracy

87.8% (3.3b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.5b

bsearch78.0ms

Steps

Iters	Range	Point
3	5.062782482725967e+112	6.853081242536654e+112	5.174676155214135e+112
2	-9.893319725742429e-275	-9.099256253469455e-275	-9.198514187503577e-275
9	-1.7523220282583258e+27	-2.534584590737501e+21	-1.7289388930153844e+27

Iters

Range

Point

5.062782482725967e+112

6.853081242536654e+112

5.174676155214135e+112

-9.893319725742429e-275

-9.099256253469455e-275

-9.198514187503577e-275

-1.7523220282583258e+27

-2.534584590737501e+21

-1.7289388930153844e+27

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	26
1	45	26

end0.0ms

sample972.0ms

Algorithm

intervals

Results

198.0ms	1057×	body	2560	valid
185.0ms	5833×	body	80	valid
132.0ms	878×	body	1280	valid
88.0ms	2890×	body	80	nan
59.0ms	458×	body	640	valid
32.0ms	138×	body	5120	valid
24.0ms	245×	body	320	valid
6.0ms	97×	body	160	valid