Details

Time bar (total: 3.4s)

sample52.0ms

Algorithm
intervals
Results
10.0ms191×body80valid
9.0ms32×body2560valid
7.0ms30×body1280valid
5.0ms97×body80nan
3.0ms14×body640valid
1.0ms3×body5120valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.2b

Counts
2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series68.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0394773
11501683
25002673

prune153.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh000
Picked101
Done000
Total74983

Merged error: 5.1b

Counts
83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.0b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.9b
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series128.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06262580
129912341
250032328

prune272.0ms

Filtered
160 candidates to 106 candidates (33.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1573160
Fresh268
Picked101
Done000
Total1609169

Merged error: 5.1b

Counts
169 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.9b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
18.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0470914
12126788
25001776

prune136.0ms

Filtered
92 candidates to 66 candidates (28.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New91192
Fresh178
Picked011
Done000
Total929101

Merged error: 5.1b

Counts
101 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.2b
(- (* b b) (* 4.0 (* a c)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
10.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
6.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
15.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0380774
11335699
25001697

prune100.0ms

Filtered
84 candidates to 60 candidates (28.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New83184
Fresh167
Picked011
Done011
Total84993

Merged error: 5.1b

Counts
93 → 9

regimes292.0ms

Accuracy

86% (4.0b remaining)

Error of 9.7b against oracle of 5.7b and baseline of 34.4b

bsearch97.0ms

Steps
ItersRangePoint
9
20888.935802105752
440947194387.52716
29404928.46343024
7
1.9211104906896484e-75
2.6007375332320908e-73
3.6548606607510087e-75
9
-1.3279209152234913e+54
-5.495259451600425e+45
-1.307112579275623e+54

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04527
14527

end0.0ms

sample1.6s

Algorithm
intervals
Results
324.0ms1062×body2560valid
310.0ms5871×body80valid
206.0ms852×body1280valid
142.0ms2848×body80nan
88.0ms452×body640valid
37.0ms246×body320valid
34.0ms97×body5120valid
12.0ms125×body160valid

Profiling

Loading profile data...