Details

Time bar (total: 5.3s)

sample42.0ms

Algorithm
intervals
Results
9.0ms40×body2560valid
7.0ms196×body80valid
4.0ms20×body1280valid
3.0ms94×body80nan
2.0ms14×body640valid
1.0ms7×body320valid
0.0ms4×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: 33.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

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:
69.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0404890
11481801
25001796

prune244.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite158.0ms

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:
109.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
9.0ms
(- (* b b) (* 4.0 (* a c)))
27.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series308.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
52.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0469991
12048866
25002857

prune233.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.3b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
12.1b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite276.0ms

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:
44.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
144.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
71.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series539.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
174.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
207.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify114.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07642421
137162067
250012044

prune390.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
1.8b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.4b
(/ (* 4.0 (* a c)) (* 2.0 a))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite92.0ms

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:
9.0ms
(- (* b b) (* 4.0 (* a c)))
47.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series221.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* 4.0 (* a c)))
87.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0403576
12221498
25001498

prune190.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.2b

regimes387.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.7b

bsearch195.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
1.2765183497133349e+91
10
1.8528783307027254e-233
2.5124863806720963e-219
2.4770647872858895e-233
10
-5.024868303916657e+156
-7.485719939656648e+141
-1.948753525425809e+142

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04826
15026
25026

end0.0ms

sample1.2s

Algorithm
intervals
Results
243.0ms1038×body2560valid
229.0ms5858×body80valid
167.0ms919×body1280valid
106.0ms2943×body80nan
67.0ms475×body640valid
29.0ms255×body320valid
26.0ms97×body5120valid
7.0ms96×body160valid