Details

Time bar (total: 5.2s)

sample41.0ms

Algorithm
intervals
Results
8.0ms38×body2560valid
6.0ms177×body80valid
4.0ms26×body1280valid
4.0ms112×body80nan
3.0ms20×body640valid
2.0ms6×body5120valid
1.0ms9×body320valid
0.0ms4×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: 34.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*r* pow-prod-down sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*l* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 76
Calls
4 calls:
6.0ms
(* (* 3.0 a) c)
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0433744
11918650
25002638

prune215.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.3b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.8b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite90.0ms

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))))
40.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
25.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
143.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
179.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify118.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
06472692
131142439
250012426

prune408.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.3b
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
9.0b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite74.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
32.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
125.0ms
(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
101.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify92.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07701662
139921314
250031302

prune260.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.8b
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) c)
5.3b
(/ (* 1 (/ 3.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) c))) (* 3.0 a))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
160×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
86×add-exp-log
75×add-cube-cbrt
54×add-cbrt-cube
45×div-exp
26×associate-/l* distribute-lft-out-- difference-of-squares
25×cbrt-undiv prod-exp
16×sqrt-prod
13×distribute-rgt-neg-in cbrt-unprod
8×1-exp add-log-exp
6×div-inv
5×pow1
4×associate-/r*
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log
Counts
4 → 194
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
38.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) c)
33.0ms
(/ (* 1 (/ 3.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) c))) (* 3.0 a))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series376.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
100.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) c)
127.0ms
(/ (* 1 (/ 3.0 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a) c))) (* 3.0 a))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify55.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010443308
150012957

prune449.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

regimes406.0ms

Accuracy

89.9% (2.8b remaining)

Error of 8.4b against oracle of 5.6b and baseline of 33.2b

bsearch164.0ms

Steps
ItersRangePoint
9
3.895668027475672e+69
5.84241073219057e+75
3.947279557993342e+70
6
-8.36501767772797e-260
-8.1135434350231975e-261
-6.347792959650586e-260
9
-3.6963232668708646e+158
-3.0922224130316533e+150
-5.737486573143019e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04729
14929
24929

end0.0ms

sample1.1s

Algorithm
intervals
Results
231.0ms1084×body2560valid
215.0ms5820×body80valid
153.0ms889×body1280valid
103.0ms2903×body80nan
68.0ms455×body640valid
27.0ms240×body320valid
26.0ms99×body5120valid
9.0ms127×body160valid