Details

Time bar (total: 5.4s)

sample57.0ms

Algorithm
intervals
Results
12.0ms274×body80nan
10.0ms145×body160valid
10.0ms530×pre80true
5.0ms50×body320valid
2.0ms61×body80valid

simplify11.0ms

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: 43.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune201.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- 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))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06422664
131752400
250032388

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
15×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
9×pow1
7×add-cube-cbrt associate-*r*
6×prod-exp cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
35.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series382.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
110.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify122.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
05221156
13447949
25002944

prune263.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 a) (- (- 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))) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
123×pow1
69×pow-prod-down
56×add-exp-log add-cbrt-cube
33×add-sqr-sqrt prod-exp cbrt-unprod
22×*-un-lft-identity times-frac
18×add-cube-cbrt
15×difference-of-squares
9×associate-*r* pow-sqr pow-prod-up associate-/l*
4×cbrt-undiv unpow-prod-down associate-*r/ div-exp associate-/r* associate-/r/ associate-/l/ add-log-exp sqr-pow
3×flip3-- pow-plus flip--
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in flip3-+ associate-*l* clear-num sqrt-prod *-commutative flip-+ div-inv distribute-lft-out--
1×pow2 distribute-rgt-neg-in div-sub swap-sqr
Counts
4 → 160
Calls
4 calls:
104.0ms
(* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
46.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))))
19.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
30.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))))
91.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
36.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08332564
150012058

prune444.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes106.0ms

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
02613
12813
22813

end0.0ms

sample1.5s

Algorithm
intervals
Results
345.0ms4927×body160valid
298.0ms16554×pre80true
283.0ms8554×body80nan
133.0ms1296×body320valid
61.0ms1777×body80valid