Details

Time bar (total: 5.1s)

sample66.0ms

Algorithm
intervals
Results
16.0ms209×body80valid
15.0ms39×body2560valid
9.0ms21×body1280valid
8.0ms107×body80nan
3.0ms10×body640valid
1.0ms4×body320valid
0.0ms3×body160valid

simplify14.0ms

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: 32.4b

localize11.0ms

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)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:
36.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 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))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404890
11481801
25001796

prune243.0ms

Pruning

9 alts after pruning (9 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)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.0b
(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:
57.0ms
(* (- (- 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))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0469991
12048866
25002857

prune244.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.8b

localize22.0ms

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)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite59.0ms

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:
35.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0404890
11481801
25001796

prune235.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
1.6b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.1b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log *-un-lft-identity add-cbrt-cube
10×add-log-exp
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
4×times-frac distribute-lft-out associate-/l*
3×cbrt-undiv flip3-+ div-exp prod-exp sqrt-prod cbrt-unprod flip-+
2×flip3-- sqrt-div associate-*l/ sum-log associate-/r/ flip-- associate-/l/
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num associate-/r* div-inv
Counts
4 → 71
Calls
4 calls:
5.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
164.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
0502969
13079812
25002794

prune221.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.8b

regimes259.0ms

Accuracy

83.5% (4.7b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 34.1b

bsearch198.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
1.6414783348607511e+125
7
-2.4269014694578893e-123
-3.257547761252762e-125
-2.3901106171036543e-123
6
-6461629.042770713
-1043668.381521804
-1519208.9305899257
4
-1.0929352752278947e+66
-7.476825112667549e+65
-8.866531255203124e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05335
15735
25735

end0.0ms

sample1.9s

Algorithm
intervals
Results
478.0ms5956×body80valid
410.0ms1049×body2560valid
291.0ms909×body1280valid
205.0ms2826×body80nan
113.0ms442×body640valid
47.0ms101×body5120valid
39.0ms199×body320valid
14.0ms102×body160valid