Details

Time bar (total: 4.5s)

sample63.0ms

Algorithm
intervals
Results
13.0ms37×body2560valid
12.0ms197×body80valid
7.0ms24×body1280valid
5.0ms77×body80nan
4.0ms16×body640valid
0.0ms4×body160valid
0.0ms2×body320valid

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: 32.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

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))
6.0ms
(- (* 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)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms
(- (* b b) (* (* 3.0 a) c))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0400780
11529686
25002675

prune259.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

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))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
47.0ms
(- (* b b) (* (* 3.0 a) c))
75.0ms
(+ (- 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 (36.0ms)

IterNodesCost
0400780
11529686
25002675

prune220.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.6b
(- (* b b) (* (* 3.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
21×add-cube-cbrt
19×associate-*r*
16×add-cbrt-cube
13×associate-*l*
10×add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1
6×unswap-sqr
4×cbrt-undiv distribute-rgt-neg-in cbrt-unprod
3×sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+l- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative flip-+
Counts
4 → 104
Calls
4 calls:
20.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
4.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
43.0ms
(- (* 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)))

simplify72.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06121234
129861078
250021068

prune279.0ms

Filtered
116 candidates to 81 candidates (69.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
21×add-cube-cbrt
19×associate-*l*
16×add-cbrt-cube
13×associate-*r*
10×add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1
6×unswap-sqr
4×cbrt-undiv distribute-rgt-neg-in cbrt-unprod
3×sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+l- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down neg-log associate-*l/ un-div-inv *-commutative flip-+
Counts
4 → 105
Calls
4 calls:
19.0ms
(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 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)))

series305.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 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)))

simplify66.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06111270
126111118
250021101

prune261.0ms

Filtered
117 candidates to 81 candidates (69.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.0b

regimes405.0ms

Accuracy

88.1% (3.3b remaining)

Error of 9.1b against oracle of 5.8b and baseline of 33.9b

bsearch138.0ms

Steps
ItersRangePoint
6
6254161.133583045
42925490.781275615
31296389.294779938
5
1.4848686600671973e-153
5.873735982633398e-153
4.6569086088577344e-153
10
-4.4721271386820616e+151
-9.712280864301115e+136
-1.1259751240381662e+137

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05634
15834
25834

end0.0ms

sample1.3s

Algorithm
intervals
Results
335.0ms853×body1280valid
236.0ms1046×body2560valid
229.0ms5939×body80valid
99.0ms2866×body80nan
61.0ms441×body640valid
30.0ms111×body5120valid
23.0ms226×body320valid
8.0ms117×body160valid