Details

Time bar (total: 6.3s)

sample74.0ms

Algorithm
intervals
Results
20.0ms181×body80valid
16.0ms38×body2560valid
11.0ms31×body1280valid
6.0ms66×body80nan
4.0ms14×body640valid
2.0ms5×body5120valid
2.0ms9×body320valid
1.0ms4×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
0.8b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

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:
36.0ms
(/ (+ (- 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))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0403779
11514685
25002674

prune228.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
9.0b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite93.0ms

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:
14.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
40.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
29.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series642.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
140.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06402692
129442439
250012426

prune430.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
24.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
123×add-exp-log
63×add-cbrt-cube
57×prod-exp
40×div-exp
25×cbrt-unprod
20×cbrt-undiv
12×add-sqr-sqrt
11×*-un-lft-identity
8×pow1 rec-exp 1-exp add-log-exp
7×add-cube-cbrt
5×associate-/r/
4×flip3-- times-frac sqrt-prod flip-- associate-/l*
2×frac-times pow-flip frac-2neg sqrt-div diff-log associate-*r/ clear-num associate-/r* div-inv distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ inv-pow
Counts
4 → 115
Calls
4 calls:
63.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07301524
140741199
250011177

prune237.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (* (/ 2.0 4.0) 1) c))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
441×times-frac
250×add-sqr-sqrt
249×*-un-lft-identity
149×add-cube-cbrt
94×add-exp-log
64×div-exp
50×distribute-lft-out-- difference-of-squares
37×div-inv
36×add-cbrt-cube
28×sqrt-prod
27×associate-/l*
25×distribute-rgt-neg-in
20×cbrt-undiv
17×associate-/r/
16×prod-exp
14×1-exp
11×flip3-- flip--
10×add-log-exp
7×associate-/r*
6×rec-exp
5×pow1
4×cbrt-unprod
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 312
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
44.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (* (/ 2.0 4.0) 1) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series320.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* 4.0 (* a c)))
124.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ (* (/ 2.0 4.0) 1) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
014116396
150015867

prune584.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

regimes151.0ms

Accuracy

87.9% (2.9b remaining)

Error of 8.9b against oracle of 6.0b and baseline of 30.0b

bsearch282.0ms

Steps
ItersRangePoint
10
9.168682727753708e+124
1.4581761209996442e+140
1.8597470564587674e+138
8
-1.154719659209351e-220
-9.703862537564153e-224
-8.703508382455323e-221
9
-3.0136667244557635e+62
-1.4072277076308412e+56
-5.4369139762720996e+56

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06140
16940
26940

end0.0ms

sample2.1s

Algorithm
intervals
Results
557.0ms5833×body80valid
461.0ms1077×body2560valid
305.0ms856×body1280valid
235.0ms2698×body80nan
131.0ms464×body640valid
49.0ms223×body320valid
48.0ms96×body5120valid
16.0ms104×body160valid