Details

Time bar (total: 5.6s)

sample60.0ms

Algorithm
intervals
Results
15.0ms201×body80valid
8.0ms21×body2560valid
7.0ms23×body1280valid
6.0ms87×body80nan
5.0ms20×body640valid
2.0ms5×body5120valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite58.0ms

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:
34.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune261.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
30.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05331804
125441605
250021531

prune257.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

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:
58.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
86.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0469991
12048866
25002857

prune223.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.1b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
2.1b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.9b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
61×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp
18×difference-of-squares
16×div-exp
13×distribute-lft-out
12×sqrt-prod
9×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 → 149
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
66.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
26.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* 4.0 (* a c)))
168.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
203.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify117.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07602359
137422008
250011985

prune379.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 8.1b

regimes294.0ms

Accuracy

86% (3.6b remaining)

Error of 9.4b against oracle of 5.8b and baseline of 31.6b

bsearch198.0ms

Steps
ItersRangePoint
7
6.184155830638016e+27
1.3306260697673677e+30
1.2919983862558445e+30
9
-2.7671842665178686e-160
-1.5330649496129563e-165
-4.369067609732386e-164
7
-2.129980745276144e+116
-9.287529331322677e+113
-9.476143455152386e+113

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04227
14227

end0.0ms

sample1.9s

Algorithm
intervals
Results
457.0ms5870×body80valid
387.0ms1038×body2560valid
281.0ms900×body1280valid
222.0ms2910×body80nan
108.0ms434×body640valid
54.0ms115×body5120valid
49.0ms260×body320valid
17.0ms127×body160valid