Details

Time bar (total: 4.8s)

sample52.0ms

Algorithm
intervals
Results
12.0ms194×body80valid
10.0ms33×body2560valid
6.0ms23×body1280valid
5.0ms96×body80nan
4.0ms18×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify12.0ms

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: 35.1b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 4.0 a) c)
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
25.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def add-log-exp
9×add-exp-log add-cube-cbrt add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative flip-+
Counts
4 → 80
Calls
4 calls:
5.0ms
(* (* 4.0 a) c)
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)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 4.0 a) c)
89.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0337530
11440479
25002467

prune230.0ms

Filtered
92 candidates to 71 candidates (77.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New87592
Fresh000
Picked101
Done000
Total88593

Merged error: 13.0b

Counts
93 → 5

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)))
25.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:
11.0ms
(/ (+ (- 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))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0438854
11658750
25001735

prune247.0ms

Filtered
102 candidates to 80 candidates (78.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New957102
Fresh314
Picked101
Done000
Total998107

Merged error: 6.8b

Counts
107 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
2.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.3b
(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)))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series439.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* 4.0 (* a c)))
145.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
177.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify111.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06652663
132592412
250012405

prune410.0ms

Filtered
170 candidates to 117 candidates (68.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1664170
Fresh347
Picked101
Done000
Total1708178

Merged error: 6.7b

Counts
178 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
13.0b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.3b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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:
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
95.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify109.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
05973032
128321946
250021857

prune246.0ms

Filtered
162 candidates to 79 candidates (48.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1611162
Fresh167
Picked101
Done000
Total1637170

Merged error: 6.7b

Counts
170 → 7

regimes156.0ms

Accuracy

92% (1.9b remaining)

Error of 7.4b against oracle of 5.4b and baseline of 29.3b

bsearch179.0ms

Steps
ItersRangePoint
7
0.008549975533169097
1.4731263457460937
1.4443031837246074
8
-1.7832961101597004e-170
-3.712432627983841e-174
-3.760762857445126e-174
9
-8.023912243850115e+115
-1.183450711292762e+109
-1.173641368412307e+114

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04726
14726

end0.0ms

sample1.5s

Algorithm
intervals
Results
343.0ms1092×body2560valid
315.0ms5847×body80valid
216.0ms875×body1280valid
147.0ms2883×body80nan
90.0ms451×body640valid
44.0ms111×body5120valid
34.0ms233×body320valid
12.0ms118×body160valid