Details

sample282.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
7.0ms	35×	body	2560	valid
4.0ms	25×	body	1280	valid
3.0ms	87×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	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: 34.0b

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 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

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:

46.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune239.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.3b	(/ (/ (+ 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)))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

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))))
43.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
30.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms	(/ (/ (+ 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)))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify119.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (87.0ms)

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

prune502.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.3b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
58.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series462.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
178.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
152.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1582	8735
1	5001	8087

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 (/ 1 c)))
1.0b	(- (* b_2 b_2) (* a c))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-exp-log`
132×	`add-sqr-sqrt`
131×	`times-frac`
89×	`*-un-lft-identity`
82×	`div-exp`
52×	`prod-exp`
51×	`add-cube-cbrt`
44×	`associate-r`
41×	`rec-exp` `1-exp`
27×	`associate-l`
25×	`add-cbrt-cube`
21×	`unswap-sqr`
10×	`add-log-exp`
9×	`pow1` `cbrt-undiv`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`sqrt-prod`
6×	`cbrt-unprod`
5×	`div-inv`
4×	`flip3--` `distribute-rgt-neg-in` `flip--`
3×	`diff-log` `pow-prod-down` `associate-/r/`
2×	`sub-neg` `pow-flip` `sqrt-div` `inv-pow`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `neg-log` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 210

Calls

4 calls:

84.0ms	(* (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 (/ 1 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)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 (/ 1 c)))
36.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1126	2508
1	4463	2092
2	5001	1966

prune352.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes187.0ms

Accuracy

93.5% (1.6b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 29.8b

bsearch112.0ms

Steps

Iters	Range	Point
6	4.706455236749836e+29	5.491842449186372e+30	5.349311795482947e+30
8	-1.2523555155265933e-243	-3.6841099953537603e-246	-6.7952690093112265e-245
7	-2.963931757502914e+119	-3.3757792073266624e+117	-5.955152059551362e+118

Iters

Range

Point

4.706455236749836e+29

5.491842449186372e+30

5.349311795482947e+30

-1.2523555155265933e-243

-3.6841099953537603e-246

-6.7952690093112265e-245

-2.963931757502914e+119

-3.3757792073266624e+117

-5.955152059551362e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample978.0ms

Algorithm

intervals

Results

203.0ms	1079×	body	2560	valid
194.0ms	5758×	body	80	valid
144.0ms	915×	body	1280	valid
86.0ms	2894×	body	80	nan
58.0ms	449×	body	640	valid
23.0ms	100×	body	5120	valid
20.0ms	223×	body	320	valid
8.0ms	133×	body	160	valid