Details

Time bar (total: 5.2s)

sample40.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
6.0ms181×body80valid
6.0ms33×body1280valid
3.0ms92×body80nan
2.0ms17×body640valid
2.0ms6×body5120valid
1.0ms6×body320valid
0.0ms2×body160valid

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: 37.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0400780
11529686
25002675

prune234.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.2b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.7b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

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:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series482.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
152.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
178.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06472692
131142439
250012426

prune452.0ms

Filtered
166 candidates to 111 candidates (66.9%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 3.0 a) c))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.1b
(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
23.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
188×times-frac
149×add-sqr-sqrt
122×*-un-lft-identity
94×add-exp-log
85×associate-*r*
80×add-cube-cbrt
58×add-cbrt-cube
49×div-exp
27×cbrt-undiv
26×associate-*l*
25×prod-exp
20×distribute-lft-out-- difference-of-squares
15×cbrt-unprod
13×sqrt-prod
10×distribute-rgt-neg-in add-log-exp
8×div-inv unswap-sqr
7×pow1 associate-/r/
6×flip3-- flip--
4×rec-exp 1-exp
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 208
Calls
4 calls:
4.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
62.0ms
(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series348.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
153.0ms
(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify54.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013273225
150022663

prune600.0ms

Filtered
220 candidates to 137 candidates (62.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
4.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
44.0ms
(- (* b b) (* (* 3.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0400780
11529686
25002675

prune206.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.9b

regimes502.0ms

Accuracy

86.1% (4.2b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 36.1b

bsearch101.0ms

Steps
ItersRangePoint
9
1.4411111155905935e-45
3.477369949839467e-39
5.998855237299608e-44
7
-4.333566438159085e+154
-4.450998173879583e+152
-4.987323159316817e+152

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03817
14017
24017

end0.0ms

sample1.1s

Algorithm
intervals
Results
225.0ms1057×body2560valid
218.0ms5836×body80valid
153.0ms878×body1280valid
98.0ms2892×body80nan
67.0ms459×body640valid
36.0ms135×body5120valid
25.0ms245×body320valid
7.0ms96×body160valid