Details

Time bar (total: 4.8s)

sample34.0ms

Algorithm
intervals
Results
15.0ms280×body80valid
4.0ms92×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.5b

localize116.0ms

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))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

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)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
0246646
1890606
23700588
35001584

prune293.0ms

Filtered
75 candidates to 60 candidates (80.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.1b

localize115.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.5b
(/ (* a c) b)
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt
8×times-frac add-log-exp
6×associate-/l*
5×pow1
4×cbrt-undiv div-exp associate-/r* sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 83
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
23.0ms
(/ (* a c) b)
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0478774
12145683
25002678

prune357.0ms

Filtered
95 candidates to 67 candidates (70.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize116.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
11.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms
(- (* 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)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0362863
11529768
25001759

prune325.0ms

Filtered
88 candidates to 63 candidates (71.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize115.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.1b
(/ (+ (- b) (- (* 2.0 (/ a (/ b c))) b)) (* 2.0 a))
4.1b
(/ a (/ b c))
23.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
61×*-un-lft-identity
54×add-sqr-sqrt
49×add-cube-cbrt
14×add-exp-log associate-/r* add-cbrt-cube
8×associate-/l* add-log-exp
6×div-inv
5×pow1 cbrt-undiv div-exp
4×sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log prod-exp associate-/r/ cbrt-unprod flip-+
Counts
4 → 132
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ (+ (- b) (- (* 2.0 (/ a (/ b c))) b)) (* 2.0 a))
6.0ms
(/ a (/ b c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series223.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms
(/ (+ (- b) (- (* 2.0 (/ a (/ b c))) b)) (* 2.0 a))
20.0ms
(/ a (/ b c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07011141
130541044
250021041

prune577.0ms

Filtered
144 candidates to 112 candidates (77.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.8b

regimes272.0ms

Accuracy

87.5% (1.8b remaining)

Error of 8.4b against oracle of 6.6b and baseline of 20.9b

bsearch126.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
6.51740022507215e+112
9
-1.7523220282583258e+27
-2.534584590737501e+21
-1.7289388930153844e+27

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06081
16081

end0.0ms

sample835.0ms

Algorithm
intervals
Results
446.0ms8706×body80valid
136.0ms2892×body80nan