Details

Time bar (total: 4.5s)

sample36.0ms

Algorithm
intervals
Results
6.0ms32×body2560valid
6.0ms184×body80valid
5.0ms29×body1280valid
3.0ms94×body80nan
3.0ms21×body640valid
1.0ms6×body5120valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1337
2467
3497
4497

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
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 → 171
Calls
4 calls:
43.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms
(- (- 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)))

series250.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms
(- (* b_2 b_2) (* a c))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05493055
118262150
250012063

prune352.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
63×*-un-lft-identity
61×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-exp-log associate-*r*
11×times-frac fma-neg
10×add-log-exp
9×add-cbrt-cube
7×pow1 neg-mul-1 associate-*l*
5×flip3-- flip--
4×expm1-log1p-u prod-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg sqrt-div div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 169
Calls
4 calls:
50.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms
(- (* b_2 b_2) (* a c))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06092985
123341993
250011940

prune316.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
61×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
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 → 171
Calls
4 calls:
42.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
19.0ms
(- (- 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)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
183 → 183
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05493055
118262150
250012063

prune324.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.2b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
165×times-frac
118×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
15×add-exp-log
11×fma-neg
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×neg-mul-1 flip3-- div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 257
Calls
4 calls:
29.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
17.0ms
(- (- 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)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07704550
132153424
250023236

prune362.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.0b

regimes274.0ms

Accuracy

80.3% (5.6b remaining)

Error of 11.0b against oracle of 5.4b and baseline of 33.9b

bsearch159.0ms

Steps
ItersRangePoint
8
9.456042252142157e+48
5.633410846004884e+51
5.5792500737545097e+51
7
-8.729222821301493e-116
-3.4297016692569784e-117
-8.637249247672526e-116
5
-2.4989029931801306e-33
-1.2234821552231479e-33
-2.374474662067348e-33
9
-2.416358248243101e+20
-517129303899.1912
-524848456042.2247

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04831
15431
25431

end0.0ms

sample971.0ms

Algorithm
intervals
Results
197.0ms1030×body2560valid
186.0ms5915×body80valid
143.0ms917×body1280valid
87.0ms2871×body80nan
56.0ms457×body640valid
24.0ms102×body5120valid
21.0ms200×body320valid
8.0ms126×body160valid