Details

Time bar (total: 5.4s)

sample54.0ms

Algorithm
intervals
Results
10.0ms537×pre80true
9.0ms143×body160valid
9.0ms281×body80nan
4.0ms45×body320valid
2.0ms68×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) c)
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
36.7b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-log-exp
9×pow1
7×add-sqr-sqrt add-cube-cbrt
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*r* pow-prod-down
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ div-exp sum-log flip-+ associate-/l/
1×+-commutative sub-neg flip3-- frac-2neg diff-log div-sub associate-*l* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 73
Calls
4 calls:
4.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(* (* 3.0 a) c)
16.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series252.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 3.0 a) c))
20.0ms
(* (* 3.0 a) c)
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify58.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0419716
11930613
25002608

prune197.0ms

Filtered
85 candidates to 59 candidates (69.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b
(* (* 3.0 a) c)
0.3b
(* 3.0 (* a c))
0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt *-un-lft-identity
40×add-cube-cbrt
30×associate-/l*
28×add-exp-log add-cbrt-cube
20×distribute-lft-out-- difference-of-squares
14×pow1
10×distribute-rgt-neg-in sqrt-prod
8×prod-exp associate-/r* cbrt-unprod
7×cbrt-undiv div-exp
6×pow-prod-down associate-/r/
4×associate-*r* associate-*l* div-inv add-log-exp
3×flip3-- div-sub flip-- associate-/l/
2×associate-+l- frac-2neg clear-num *-commutative
1×flip3-+ flip-+
Counts
4 → 159
Calls
4 calls:
29.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms
(* (* 3.0 a) c)
5.0ms
(* 3.0 (* a c))
31.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series331.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0ms
(* (* 3.0 a) c)
20.0ms
(* 3.0 (* a c))
126.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify111.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
06843100
133072567
250012533

prune480.0ms

Filtered
171 candidates to 107 candidates (62.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b
(* (* 3.0 a) c)
0.3b
(* (* 3.0 a) c)
0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt *-un-lft-identity
40×add-cube-cbrt
30×associate-/l*
28×add-exp-log add-cbrt-cube
20×distribute-lft-out-- difference-of-squares
14×pow1
10×distribute-rgt-neg-in sqrt-prod
8×prod-exp associate-/r* cbrt-unprod
7×cbrt-undiv div-exp
6×associate-*r* pow-prod-down associate-/r/
4×div-inv add-log-exp
3×flip3-- div-sub flip-- associate-/l/
2×associate-+l- frac-2neg associate-*l* clear-num *-commutative
1×flip3-+ flip-+
Counts
4 → 159
Calls
4 calls:
26.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms
(* (* 3.0 a) c)
5.0ms
(* (* 3.0 a) c)
35.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series337.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms
(* (* 3.0 a) c)
20.0ms
(* (* 3.0 a) c)
130.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify109.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06273101
131392568
250012534

prune460.0ms

Filtered
171 candidates to 105 candidates (61.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c)))
0.3b
(/ (/ (- (* (- (pow b 2) (pow b 2)) (- (pow b 2) (pow b 2))) (* (* (* 3.0 a) c) (* (* 3.0 a) c))) (* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c)))) (* 3.0 a))
0.4b
(/ (- (* (- (pow b 2) (pow b 2)) (- (pow b 2) (pow b 2))) (* (* (* 3.0 a) c) (* (* 3.0 a) c))) (* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c))))
0.5b
(* (* (* 3.0 a) c) (* (* 3.0 a) c))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
120×pow1
68×add-exp-log add-cbrt-cube
67×pow-prod-down
34×prod-exp cbrt-unprod
22×times-frac
18×add-sqr-sqrt
16×*-un-lft-identity
14×associate-/l*
12×cbrt-undiv add-cube-cbrt div-exp
9×pow-sqr pow-prod-up
8×associate-*l* associate-*l/
7×associate-*r*
6×associate-/r/ difference-of-squares
5×flip3-- flip--
4×div-inv add-log-exp
3×pow-plus div-sub associate-/l/
2×distribute-rgt-neg-in frac-2neg clear-num associate-/r* *-commutative distribute-lft-out--
1×pow2 distribute-lft-neg-in neg-mul-1 swap-sqr sqrt-prod distribute-rgt-neg-out unswap-sqr
Counts
4 → 161
Calls
4 calls:
14.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c)))
38.0ms
(/ (/ (- (* (- (pow b 2) (pow b 2)) (- (pow b 2) (pow b 2))) (* (* (* 3.0 a) c) (* (* 3.0 a) c))) (* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c)))) (* 3.0 a))
37.0ms
(/ (- (* (- (pow b 2) (pow b 2)) (- (pow b 2) (pow b 2))) (* (* (* 3.0 a) c) (* (* 3.0 a) c))) (* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c))))
12.0ms
(* (* (* 3.0 a) c) (* (* 3.0 a) c))

series459.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c)))
133.0ms
(/ (/ (- (* (- (pow b 2) (pow b 2)) (- (pow b 2) (pow b 2))) (* (* (* 3.0 a) c) (* (* 3.0 a) c))) (* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c)))) (* 3.0 a))
174.0ms
(/ (- (* (- (pow b 2) (pow b 2)) (- (pow b 2) (pow b 2))) (* (* (* 3.0 a) c) (* (* 3.0 a) c))) (* (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (- (* (* 3.0 a) c))))
36.0ms
(* (* (* 3.0 a) c) (* (* 3.0 a) c))

simplify175.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (146.0ms)

IterNodesCost
08053386
148382425
250012392

prune404.0ms

Filtered
173 candidates to 94 candidates (54.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes179.0ms

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
03024
14324
24424
34424

end0.0ms

sample1.5s

Algorithm
intervals
Results
317.0ms4746×body160valid
312.0ms16469×pre80true
265.0ms8469×body80nan
143.0ms1449×body320valid
59.0ms1805×body80valid