Details

Time bar (total: 5.8s)

sample42.0ms

Algorithm
intervals
Results
9.0ms186×body80valid
7.0ms33×body2560valid
4.0ms28×body1280valid
3.0ms86×body80nan
2.0ms15×body640valid
1.0ms5×body5120valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

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))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite107.0ms

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:
66.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
10.0ms
(- (* b b) (* (* 3.0 a) c))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms
(- (* b b) (* (* 3.0 a) c))
70.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
61.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0400780
11529686
25002675

prune218.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.4b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite180.0ms

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:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
84.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
57.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
135.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
163.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
64.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06472692
131142439
250012426

prune412.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.3b
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite123.0ms

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:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
42.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
135.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
167.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
66.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify127.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
07022050
144191582
250021541

prune318.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
11.5b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
179×add-sqr-sqrt
178×*-un-lft-identity
118×add-cube-cbrt
45×associate-/l*
41×add-exp-log
30×distribute-lft-out-- difference-of-squares
24×div-exp
23×add-cbrt-cube
18×sqrt-prod div-inv
15×distribute-rgt-neg-in
11×cbrt-undiv
8×add-log-exp
5×pow1
4×prod-exp associate-/r* associate-/r/
3×rec-exp flip3-- 1-exp flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 245
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
78.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
64.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
115.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
67.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
257 → 257
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011524329
150013977

prune520.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

regimes490.0ms

Accuracy

90.6% (2.5b remaining)

Error of 8.1b against oracle of 5.7b and baseline of 31.8b

bsearch166.0ms

Steps
ItersRangePoint
7
7.363656180201337e+60
1.0503009045500217e+63
5.354608489416471e+62
7
1.3148169546496053e-135
1.6902561201493824e-133
2.4967447941335268e-135
10
-1.6375536470903724e+107
-1.9877314958440015e+97
-1.2574766781276779e+107

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04932
14932

end0.0ms

sample1.1s

Algorithm
intervals
Results
212.0ms1051×body2560valid
207.0ms5865×body80valid
159.0ms933×body1280valid
93.0ms2815×body80nan
60.0ms452×body640valid
32.0ms113×body5120valid
25.0ms237×body320valid
8.0ms117×body160valid