Details

Time bar (total: 5.6s)

sample72.0ms

Algorithm
intervals
Results
18.0ms195×body80valid
17.0ms33×body2560valid
10.0ms27×body1280valid
6.0ms65×body80nan
3.0ms5×body5120valid
3.0ms10×body640valid
1.0ms6×body320valid
0.0ms3×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
39.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0404890
11481801
25001796

prune254.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
62.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0469991
12048866
25002857

prune239.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.9b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
7.5b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
63×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp difference-of-squares
16×div-exp
13×sqrt-prod distribute-lft-out
10×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 152
Calls
4 calls:
20.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
28.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series518.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
162.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
204.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify116.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
07642421
137162067
250012044

prune400.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.7b
(/ (* 4.0 (* a c)) (* 2.0 a))
23.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0403576
12221498
25001498

prune178.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes219.0ms

Accuracy

87.9% (3.2b remaining)

Error of 9.1b against oracle of 5.9b and baseline of 32.3b

bsearch202.0ms

Steps
ItersRangePoint
10
9.168682727753708e+124
1.4581761209996442e+140
1.4730776072485394e+128
8
-1.3367325642636083e-146
-2.3277490211177517e-150
-4.1695928252236307e-150
4
-6.724232630370945e+156
-3.4624365171705646e+156
-3.564367645708077e+156

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04125
14125

end0.0ms

sample2.0s

Algorithm
intervals
Results
539.0ms5911×body80valid
451.0ms1057×body2560valid
303.0ms865×body1280valid
227.0ms2712×body80nan
121.0ms434×body640valid
53.0ms93×body5120valid
45.0ms208×body320valid
18.0ms118×body160valid