Details

Time bar (total: 5.0s)

sample44.0ms

Algorithm
intervals
Results
11.0ms43×body2560valid
7.0ms178×body80valid
5.0ms26×body1280valid
3.0ms84×body80nan
2.0ms14×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

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-/l*
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-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
34.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0404890
11481801
25001796

prune253.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
54.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify59.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0469991
12048866
25002857

prune244.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

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:
22.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series585.0ms

Counts
4 → 12
Calls
4 calls:
388.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0361863
11479768
25002759

prune228.0ms

Filtered
88 candidates to 63 candidates (71.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.4b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
4.2b
(/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
7.3b
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
30×associate-/r*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r/
6×add-log-exp
5×pow1 flip3-- flip--
4×div-inv associate-/l*
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
25.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series405.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
87.0ms
(/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
206.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06272259
132962037
250032034

prune388.0ms

Filtered
150 candidates to 107 candidates (71.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.4b

regimes217.0ms

Accuracy

87% (3.6b remaining)

Error of 8.9b against oracle of 5.3b and baseline of 32.8b

bsearch208.0ms

Steps
ItersRangePoint
9
8.465625442272063e+58
8.825425083170634e+65
8.633216037833923e+65
10
-7.492140743585697e-204
-4.119745624249939e-214
-8.143231117685541e-211
8
-183484304836700.72
-121429039431.98735
-73773484249037.31

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04831
14831

end0.0ms

sample1.2s

Algorithm
intervals
Results
254.0ms1040×body2560valid
247.0ms5928×body80valid
181.0ms903×body1280valid
119.0ms2982×body80nan
69.0ms437×body640valid
32.0ms108×body5120valid
25.0ms213×body320valid
9.0ms110×body160valid