Details

Time bar (total: 4.9s)

sample44.0ms

Algorithm
intervals
Results
7.0ms189×body80valid
6.0ms28×body2560valid
6.0ms34×body1280valid
5.0ms7×body5120valid
3.0ms92×body80nan
2.0ms16×body640valid
0.0ms4×body160valid
0.0ms2×body320valid

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: 35.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.1b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

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))
11.0ms
(+ (- 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))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
83.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0403779
11514685
25002674

prune239.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* 4.0 (* a c)))
2.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite85.0ms

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×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 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* 4.0 (* a c)))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
186.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06282579
129542333
250012320

prune406.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
16.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series211.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0413627
12231543
25001535

prune222.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
25.1b
(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:
39.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms
(- (- 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))))

series378.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
011682503
150012016

prune295.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.8b

regimes206.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.8b against oracle of 5.8b and baseline of 29.9b

bsearch160.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
3.771181145902542e+84
9
6.841012161467506e-264
8.954106309325026e-259
7.170478586447025e-264
8
-3.734333779790662e+128
-2.2987999557012895e+125
-5.238946631357967e+127

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04727
14927
24927

end0.0ms

sample1.4s

Algorithm
intervals
Results
267.0ms457×body640valid
250.0ms1050×body2560valid
241.0ms5875×body80valid
173.0ms905×body1280valid
107.0ms2863×body80nan
28.0ms99×body5120valid
24.0ms212×body320valid
10.0ms128×body160valid