Details

Time bar (total: 6.7s)

sample56.0ms

Algorithm
intervals
Results
13.0ms122×body320valid
9.0ms484×pre80true
8.0ms228×body80nan
6.0ms88×body160valid
2.0ms15×body640valid
1.0ms31×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite54.0ms

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))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674

prune193.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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))

rewrite93.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series455.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
180.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
150.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify113.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06422664
131752400
250022388

prune415.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))
0.5b
(/ (- (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)))

rewrite254.0ms

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:
76.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
114.0ms
(/ (/ (+ 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))
23.0ms
(/ (- (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)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
184.0ms
(/ (/ (+ 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)))
37.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09935277
150014702

prune698.0ms

Filtered
247 candidates to 145 candidates (58.7%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize22.0ms

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)))))) (/ 1 (* 2.0 a)))
0.5b
(/ (- (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)))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
120×pow1
104×add-sqr-sqrt
89×add-exp-log
77×times-frac
70×*-un-lft-identity
67×pow-prod-down
65×add-cbrt-cube
47×prod-exp
42×add-cube-cbrt
35×cbrt-unprod
33×difference-of-squares
31×associate-*l*
17×div-exp
14×sqrt-prod distribute-lft-out--
11×associate-/r*
9×cbrt-undiv pow-sqr pow-prod-up associate-/l*
8×associate-*r*
7×distribute-rgt-neg-in
6×associate-/r/
4×unpow-prod-down rec-exp 1-exp div-inv associate-/l/ add-log-exp sqr-pow
3×flip3-- pow-plus flip--
2×frac-2neg flip3-+ clear-num *-commutative flip-+ unswap-sqr
1×pow2 frac-times div-sub associate-*r/ swap-sqr associate-*l/ un-div-inv
Counts
4 → 227
Calls
4 calls:
74.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
157.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (/ 1 (* 2.0 a)))
19.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
33.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
182.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (/ 1 (* 2.0 a)))
89.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
41.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010784666
150024041

prune645.0ms

Filtered
239 candidates to 132 candidates (55.2%)
Pruning

7 alts after pruning (5 fresh and 2 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
03121
13421
23421

end0.0ms

sample1.7s

Algorithm
intervals
Results
394.0ms3684×body320valid
307.0ms16437×pre80true
289.0ms8437×body80nan
209.0ms2906×body160valid
71.0ms504×body640valid
32.0ms906×body80valid