Details

Time bar (total: 5.5s)

sample42.0ms

Algorithm
intervals
Results
11.0ms201×body80valid
6.0ms31×body1280valid
5.0ms21×body2560valid
4.0ms103×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0438854
11702750
25001735

prune291.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 2.0 a)))
1.0b
(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
48×*-un-lft-identity
36×times-frac
32×add-cube-cbrt
20×sqrt-prod
19×prod-diff
16×difference-of-squares
8×distribute-lft-out-- add-log-exp
7×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×expm1-log1p-u flip3-- fma-neg flip-- log1p-expm1-u
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp clear-num div-inv
Counts
4 → 136
Calls
4 calls:
10.0ms
(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 2.0 a)))
6.0ms
(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (- b (sqrt (- (* b b) (* (* 4.0 a) c)))) (- (* 2.0 a)))
78.0ms
(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05712159
122691775
250011756

prune495.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (- (* 2.0 a)) (- b (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
270×times-frac
214×add-sqr-sqrt
163×*-un-lft-identity
113×add-cube-cbrt
50×difference-of-squares
42×associate-/r*
37×sqrt-prod
25×distribute-lft-out--
24×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
19×prod-diff
15×add-exp-log
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u fma-neg log1p-expm1-u
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 265
Calls
4 calls:
14.0ms
(/ 1 (/ (- (* 2.0 a)) (- b (sqrt (- (* b b) (* (* 4.0 a) c))))))
6.0ms
(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ 1 (/ (- (* 2.0 a)) (- b (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms
(- b (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify127.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09354716
145534041
250014036

prune557.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u 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 → 232
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
16.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify146.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08295119
137633863
250013860

prune554.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

regimes180.0ms

Accuracy

86.7% (3.8b remaining)

Error of 9.3b against oracle of 5.5b and baseline of 34.1b

bsearch163.0ms

Steps
ItersRangePoint
2
3.9431530817676045e+109
4.557375181159837e+109
4.019930844191633e+109
9
8.821301774413145e-82
2.0920398247873342e-75
8.930527750856993e-82
10
-1.5405955983178716e+163
-1.402598515452623e+153
-2.3044033969831823e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05547
15747
25747

end0.0ms

sample1.2s

Algorithm
intervals
Results
258.0ms1101×body2560valid
246.0ms5850×body80valid
182.0ms921×body1280valid
111.0ms2888×body80nan
70.0ms450×body640valid
30.0ms103×body5120valid
25.0ms228×body320valid
9.0ms121×body160valid