Details

Time bar (total: 5.0s)

sample47.0ms

Algorithm
intervals
Results
11.0ms206×body80valid
8.0ms26×body2560valid
6.0ms25×body1280valid
4.0ms75×body80nan
2.0ms12×body640valid
1.0ms8×body320valid
1.0ms5×body160valid
0.0ms1×body5120valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

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: 32.2b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
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)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0403779
11514685
25002674

prune211.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74882
Fresh000
Picked011
Done000
Total74983

Merged error: 6.0b

Counts
83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
18.0ms
(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 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))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
84.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0479920
12139790
25002777

prune211.0ms

Filtered
92 candidates to 65 candidates (70.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New89392
Fresh437
Picked011
Done011
Total938101

Merged error: 6.0b

Counts
101 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* a c)))
11.7b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log
1×+-commutative neg-sub0 associate-+l- sub-neg flip3-+ diff-log neg-log flip-+
Counts
4 → 55
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (124.0ms)

IterNodesCost
0247648
1972537
24235523
35001520

prune214.0ms

Filtered
67 candidates to 54 candidates (80.6%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New66167
Fresh145
Picked011
Done022
Total67875

Merged error: 6.0b

Counts
75 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (/ (* 4.0 (* a c)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))) (/ 1 (* 2.0 a)))
2.2b
(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
10.8b
(/ (* 4.0 (* a c)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
131×add-exp-log
67×add-cbrt-cube
64×prod-exp
40×div-exp
31×*-un-lft-identity
28×cbrt-unprod
27×times-frac
20×cbrt-undiv add-sqr-sqrt
18×associate-*l*
17×add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in associate-/r*
8×rec-exp 1-exp
7×pow1 associate-*r* distribute-lft-out
6×add-log-exp
4×associate-/r/ distribute-neg-frac
3×neg-mul-1 flip3-+ sqrt-prod flip-+ div-inv
2×sqrt-div
1×+-commutative frac-times rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ clear-num sum-log un-div-inv *-commutative flip-- associate-/l* unswap-sqr
Counts
4 → 149
Calls
4 calls:
23.0ms
(* (/ (* 4.0 (* a c)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))) (/ 1 (* 2.0 a)))
5.0ms
(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ (* 4.0 (* a c)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ (* 4.0 (* a c)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))) (/ 1 (* 2.0 a)))
85.0ms
(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
191.0ms
(/ (* 4.0 (* a c)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify117.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08742232
146861796
250011796

prune293.0ms

Filtered
161 candidates to 95 candidates (59.0%)
Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New1592161
Fresh134
Picked011
Done033
Total1609169

Merged error: 6.0b

Counts
169 → 9

regimes273.0ms

Accuracy

89.3% (3.0b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 33.9b

bsearch218.0ms

Steps
ItersRangePoint
7
6.011887282010727e+43
5.675568733030414e+45
1.9326867649712656e+45
10
6.366270423089047e-197
5.678081784027156e-185
3.222850649891201e-188
9
-3.270551254255918e+118
-2.1334538400483563e+110
-1.206809493629299e+115

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04828
14928
24928

end0.0ms

sample1.5s

Algorithm
intervals
Results
336.0ms1057×body2560valid
331.0ms5898×body80valid
236.0ms873×body1280valid
156.0ms2907×body80nan
92.0ms447×body640valid
40.0ms108×body5120valid
35.0ms229×body320valid
11.0ms107×body160valid

Profiling

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