Details

Time bar (total: 5.5s)

sample41.0ms

Algorithm
intervals
Results
8.0ms28×body2560valid
6.0ms183×body80valid
5.0ms29×body1280valid
3.0ms89×body80nan
3.0ms22×body640valid
1.0ms5×body5120valid
0.0ms7×body160valid
0.0ms1×body320valid

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: 36.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite161.0ms

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:
100.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
16.0ms
(- (* b b) (* (* 3.0 a) c))
33.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
51.0ms
(- (* b b) (* (* 3.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0400780
11529686
25002675

prune231.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.1b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.0b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite188.0ms

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:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
87.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
61.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
158.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
192.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
77.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify124.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
06472692
131142439
250012426

prune430.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.1b
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
10.8b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
86×add-exp-log
54×add-cbrt-cube
40×div-exp
30×prod-exp
22×cbrt-undiv
20×add-sqr-sqrt
19×*-un-lft-identity
16×cbrt-unprod
8×times-frac 1-exp associate-/l* add-log-exp
7×add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
3×flip3-- distribute-rgt-neg-in flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub associate-*r/ neg-log
Counts
4 → 107
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
64.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
134.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
108.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
77.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify98.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07701662
139921314
250031302

prune268.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
1.0b
(- (* b b) (* (* 3.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite144.0ms

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:
96.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
9.0ms
(- (* b b) (* (* 3.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
52.0ms
(- (* b b) (* (* 3.0 a) c))
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify75.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06121234
129861078
250021068

prune276.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.5b

regimes327.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.0b

bsearch104.0ms

Steps
ItersRangePoint
7
2.7637149443965607e-30
2.267024976733402e-28
8.955698051059873e-30
10
-5.024868303916657e+156
-7.485719939656648e+141
-2.675733832275466e+144

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03917
13917

end0.0ms

sample1.2s

Algorithm
intervals
Results
217.0ms1058×body2560valid
207.0ms5791×body80valid
161.0ms934×body1280valid
102.0ms2915×body80nan
61.0ms456×body640valid
25.0ms101×body5120valid
22.0ms224×body320valid
8.0ms112×body160valid