Details

Time bar (total: 8.2s)

sample63.0ms

Algorithm
intervals
Results
14.0ms297×body80nan
12.0ms161×body160valid
10.0ms553×pre80true
5.0ms41×body320valid
2.0ms54×body80valid

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: 44.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25002674

prune200.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series478.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify118.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
06422664
131752400
250022388

prune447.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite261.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
78.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
120.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
20.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
31.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
226.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
191.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
92.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
42.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09935284
150024705

prune719.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
0.3b
(/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
0.3b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
0.5b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite695.0ms

Algorithm
rewrite-expression-head
Rules
723×times-frac
532×add-sqr-sqrt
348×sqrt-prod
302×*-un-lft-identity
278×add-cube-cbrt
195×difference-of-squares
118×pow1
93×associate-/l*
66×pow-prod-down
59×add-exp-log add-cbrt-cube
49×unpow-prod-down sqr-pow
29×prod-exp cbrt-unprod
22×associate-/r/
18×sqrt-div
13×associate-/r*
12×div-inv distribute-lft-out--
10×cbrt-undiv div-exp
9×flip3-+ pow-sqr pow-prod-up flip-+
6×distribute-rgt-neg-in
4×associate-/l/ add-log-exp
3×flip3-- frac-2neg pow-plus div-sub clear-num flip--
1×pow2 swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 553
Calls
4 calls:
564.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
36.0ms
(/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
24.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
31.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
92.0ms
(/ (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
108.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (sqrt (+ (* b b) (* (* 4.0 a) c))))
45.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify174.0ms

Algorithm
egg-herbie
Counts
565 → 565
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0180817463
1500216350

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03638
13938
23938

end0.0ms

sample1.6s

Algorithm
intervals
Results
376.0ms4850×body160valid
306.0ms16215×pre80true
302.0ms8215×body80nan
151.0ms1326×body320valid
69.0ms1824×body80valid