Details

Time bar (total: 6.3s)

sample45.0ms

Algorithm
intervals
Results
11.0ms35×body2560valid
7.0ms186×body80valid
5.0ms25×body1280valid
3.0ms82×body80nan
2.0ms8×body5120valid
2.0ms13×body640valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
50.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405780
11563685
25001674

prune234.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series483.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06512692
131392439
250022426

prune642.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- 0 (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
8.6b
(/ (+ 0 (* 4.0 (* a c))) (- 0 (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
78×times-frac
57×add-sqr-sqrt
36×add-cube-cbrt
27×associate-/l*
20×distribute-lft-out--
18×add-exp-log add-cbrt-cube
11×distribute-lft-out
10×difference-of-squares
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1
4×flip3-- flip-- div-inv
3×sqrt-prod associate-/l/
2×frac-2neg flip3-+ sqrt-div prod-exp clear-num cbrt-unprod flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 138
Calls
4 calls:
7.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- 0 (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
49.0ms
(/ (+ 0 (* 4.0 (* a c))) (- 0 (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- 0 (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
180.0ms
(/ (+ 0 (* 4.0 (* a c))) (- 0 (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify202.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (182.0ms)

IterNodesCost
06842364
136802128
250012124

prune437.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
13.9b
(/ (* 4.0 (* a c)) (* a (- (sqrt 0) (sqrt (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
9×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity
6×pow1 cbrt-undiv add-cube-cbrt div-exp sqrt-prod add-log-exp
4×sqrt-div
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-/r/
1×+-commutative frac-2neg flip3-+ times-frac clear-num associate-/r* sum-log flip-+ div-inv distribute-lft-out associate-/l*
Counts
4 → 69
Calls
4 calls:
7.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms
(/ (* 4.0 (* a c)) (* a (- (sqrt 0) (sqrt (+ 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)))

series866.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
636.0ms
(/ (* 4.0 (* a c)) (* a (- (sqrt 0) (sqrt (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify77.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05491008
13015778
25001770

prune346.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes181.0ms

Accuracy

84.5% (3.8b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 30.1b

bsearch181.0ms

Steps
ItersRangePoint
0
3459389182982077.0
3464539799267021.5
3461964491124549.0
10
2.3277886138963038e-219
9.783824848491128e-206
2.359132365542488e-219
11
-1.1860998636736231e+119
-1.6133553378404837e+99
-1.6406413729723635e+109

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06850
17050
27050

end0.0ms

sample1.2s

Algorithm
intervals
Results
265.0ms1073×body2560valid
245.0ms5835×body80valid
180.0ms903×body1280valid
115.0ms2961×body80nan
74.0ms451×body640valid
30.0ms259×body320valid
27.0ms90×body5120valid
9.0ms118×body160valid