Details

Time bar (total: 5.1s)

sample57.0ms

Algorithm
intervals
Results
14.0ms194×body80valid
11.0ms30×body2560valid
7.0ms100×body80nan
6.0ms28×body1280valid
3.0ms14×body640valid
1.0ms8×body320valid
1.0ms6×body160valid
1.0ms2×body5120valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.9b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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:
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0403779
11514685
25002674

prune239.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.7b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×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 → 154
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series477.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
180.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify108.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06402692
129442439
250012426

prune420.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.9b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0413627
12231543
25001535

prune212.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
295×add-exp-log
166×div-exp
119×prod-exp
64×1-exp
60×add-cbrt-cube
34×rec-exp
31×times-frac
26×cbrt-undiv
24×add-sqr-sqrt
23×*-un-lft-identity
19×add-cube-cbrt
18×cbrt-unprod
14×associate-/r/
13×associate-/l*
11×frac-times
10×add-log-exp
8×flip3-- flip--
7×associate-*l/
5×pow1 associate-*r/
4×sqrt-prod
3×diff-log un-div-inv div-inv
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r* associate-/l/
Counts
4 → 179
Calls
4 calls:
35.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
011682503
150012016

prune298.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.5b

regimes171.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 29.8b

bsearch170.0ms

Steps
ItersRangePoint
5
3.0336165705843857e+124
7.533619617198572e+124
3.0781255133678807e+124
7
-3.9106408528448323e-240
-1.785276478006513e-242
-1.8135608595479747e-242
9
-8.769455893714235e+71
-3.4877376356874454e+65
-5.42705832741983e+68

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.6s

Algorithm
intervals
Results
425.0ms5937×body80valid
286.0ms1019×body2560valid
202.0ms879×body1280valid
199.0ms2907×body80nan
84.0ms438×body640valid
39.0ms116×body5120valid
37.0ms250×body320valid
12.0ms106×body160valid