Details

Time bar (total: 4.9s)

sample34.0ms

Algorithm
intervals
Results
14.0ms282×body80valid
4.0ms94×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.1b

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
0246646
1890606
23700588
35001584

prune283.0ms

Filtered
75 candidates to 60 candidates (80.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.9b

localize114.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.9b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
5.5b
(/ (* a c) b)
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp sqrt-prod
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log
Counts
4 → 77
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
22.0ms
(/ (* a c) b)
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0450688
12176609
25001607

prune331.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize116.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ a (/ b c))
4.9b
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
54×add-sqr-sqrt
53×*-un-lft-identity
49×add-cube-cbrt
16×associate-/r*
14×add-exp-log add-cbrt-cube
8×add-log-exp
6×div-inv
5×pow1 cbrt-undiv div-exp
4×sqrt-prod associate-/l*
3×flip3-- associate-/r/ flip--
2×frac-2neg sqrt-div diff-log clear-num distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod
Counts
4 → 126
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(/ a (/ b c))
11.0ms
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ a (/ b c))
66.0ms
(/ (* 2.0 c) (- (* 2.0 (/ a (/ b c))) (* 2 b)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06721055
13105970
25001970

prune576.0ms

Filtered
138 candidates to 110 candidates (79.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize118.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ a (/ b c))
4.9b
(* (* 2.0 c) (/ 1 (- (* 2.0 (/ a (/ b c))) (* 2 b))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
59×add-sqr-sqrt
58×*-un-lft-identity
54×add-cube-cbrt
31×add-exp-log
21×add-cbrt-cube
15×associate-*r*
13×associate-/r*
12×prod-exp
10×pow1
8×add-log-exp
7×div-exp
6×cbrt-unprod div-inv
5×cbrt-undiv
4×sqrt-prod
3×flip3-- pow-prod-down associate-/r/ flip-- associate-/l*
2×rec-exp sqrt-div diff-log 1-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l* neg-log clear-num un-div-inv *-commutative
Counts
4 → 143
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms
(/ a (/ b c))
15.0ms
(* (* 2.0 c) (/ 1 (- (* 2.0 (/ a (/ b c))) (* 2 b))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ a (/ b c))
66.0ms
(* (* 2.0 c) (/ 1 (- (* 2.0 (/ a (/ b c))) (* 2 b))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08001223
138321089
250011076

prune584.0ms

Filtered
155 candidates to 115 candidates (74.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.8b

regimes207.0ms

Accuracy

93.2% (1.0b remaining)

Error of 7.9b against oracle of 7.0b and baseline of 21.0b

bsearch124.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
5.846038190143142e+112
9
-1.4509995558059801e+125
-2.2693772293991552e+117
-2.0236229236168638e+122

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06261
16261

end0.0ms

sample841.0ms

Algorithm
intervals
Results
450.0ms8755×body80valid
137.0ms2908×body80nan