Details

Time bar (total: 5.9s)

sample55.0ms

Algorithm
intervals
Results
13.0ms196×body80valid
10.0ms37×body2560valid
6.0ms28×body1280valid
4.0ms91×body80nan
2.0ms12×body640valid
1.0ms5×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b
(- (* b b) (* (* 3.0 a) c))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b
(sqrt (- (* b b) (* (* 3.0 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:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
2.0ms
(- (* b b) (* (* 3.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0400780
11529686
25002675

prune211.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.5b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite94.0ms

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) (* (* 3.0 a) c))))
41.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
29.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
146.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
187.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06472692
131142439
250012426

prune412.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
7.5b
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
26×times-frac
22×add-sqr-sqrt
21×*-un-lft-identity
19×cbrt-undiv div-exp
18×prod-exp cbrt-unprod
17×add-cube-cbrt
10×associate-*r/ associate-/r/
8×associate-/l* add-log-exp
7×flip3-- flip--
6×div-inv
5×pow1
4×associate-/r* sqrt-prod
2×frac-2neg sqrt-div diff-log clear-num distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 116
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
17.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
151.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
179.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
07022050
144191582
250021541

prune352.0ms

Filtered
128 candidates to 87 candidates (68.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (- (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (- a))
7.5b
(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
461×times-frac
261×distribute-rgt-neg-in
256×add-sqr-sqrt
255×*-un-lft-identity
236×distribute-lft-neg-in
155×add-cube-cbrt
50×distribute-lft-out-- difference-of-squares
46×associate-/r/
42×neg-mul-1
31×associate-/l*
28×sqrt-prod
25×flip3-- flip--
24×div-inv
17×associate-/r*
11×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1
3×cbrt-undiv div-exp
2×neg-sub0 frac-2neg sqrt-div diff-log clear-num
1×associate--l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub distribute-frac-neg neg-log prod-exp cbrt-unprod associate-/l/ distribute-neg-frac
Counts
4 → 419
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
75.0ms
(/ (- (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (- a))
22.0ms
(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series479.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
145.0ms
(/ (- (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (- a))
180.0ms
(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify98.0ms

Algorithm
egg-herbie
Counts
431 → 431
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
014628699
150018214

prune975.0ms

Filtered
431 candidates to 270 candidates (62.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

regimes157.0ms

Accuracy

90.4% (2.5b remaining)

Error of 7.8b against oracle of 5.3b and baseline of 31.4b

bsearch154.0ms

Steps
ItersRangePoint
8
2.531505514381809e+64
5.72577144612764e+68
3.2694478559846486e+65
7
-1.1954255748660408e-254
-7.328840644673834e-256
-1.3555670582517698e-255
7
-4.788437381304621e+112
-1.2414549986870086e+111
-2.8688546137715554e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04928
15328
25328

end0.0ms

sample1.1s

Algorithm
intervals
Results
241.0ms1121×body2560valid
212.0ms5763×body80valid
151.0ms856×body1280valid
101.0ms2821×body80nan
63.0ms452×body640valid
36.0ms128×body5120valid
25.0ms252×body320valid
8.0ms122×body160valid