Details

Time bar (total: 4.9s)

sample43.0ms

Algorithm
intervals
Results
10.0ms33×body2560valid
7.0ms183×body80valid
6.0ms31×body1280valid
3.0ms85×body80nan
2.0ms17×body640valid
1.0ms9×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.4b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(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))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
74.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25001735

prune273.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New9210102
Fresh000
Picked101
Done000
Total9310103

Merged error: 7.9b

Counts
103 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series609.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 4.0 a) c))
143.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
353.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify122.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
06742663
134622412
250012406

prune382.0ms

Filtered
170 candidates to 117 candidates (68.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1664170
Fresh369
Picked101
Done000
Total17010180

Merged error: 7.8b

Counts
180 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
15.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 150
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify96.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06103042
130781945
250021857

prune284.0ms

Filtered
162 candidates to 79 candidates (48.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1602162
Fresh279
Picked101
Done000
Total1639172

Merged error: 7.8b

Counts
172 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 0.5 c) (- (- 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))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
144×add-sqr-sqrt
138×*-un-lft-identity
130×add-cube-cbrt
95×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
13×associate-*l*
11×fma-neg
10×times-frac add-log-exp
9×add-exp-log add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sqrt-div associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 289
Calls
4 calls:
23.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(- (- 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)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify134.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
09278466
135705475
250025159

prune328.0ms

Filtered
301 candidates to 106 candidates (35.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2992301
Fresh178
Picked101
Done000
Total3019310

Merged error: 7.8b

Counts
310 → 9

regimes190.0ms

Accuracy

94.4% (1.3b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 30.0b

bsearch206.0ms

Steps
ItersRangePoint
8
3.182319375801986e+130
1.3165557463351014e+133
1.4487681671356545e+131
10
-3.794709535053859e-185
-7.043002195311016e-204
-4.928841649337541e-202
9
-9.104669698408525e+86
-9.304287469108188e+80
-1.6507510594910507e+86

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05538
16638
27038
37038

end0.0ms

sample1.1s

Algorithm
intervals
Results
250.0ms1068×body2560valid
239.0ms5876×body80valid
165.0ms882×body1280valid
106.0ms2898×body80nan
65.0ms446×body640valid
28.0ms103×body5120valid
24.0ms220×body320valid
8.0ms115×body160valid