Details

Time bar (total: 8.5s)

sample128.0ms

Algorithm
intervals
Results
71.0ms936×body80nan
26.0ms292×body80valid

simplify94.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02710
17210
219210
343710
481610
5157810
6276410
7500210

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
0.1b
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
26×*-un-lft-identity times-frac
24×add-cube-cbrt associate-*l*
13×add-exp-log add-cbrt-cube
11×pow1
8×associate-*r/ sqrt-prod
6×flip3-- sqrt-div associate-*r* flip--
4×frac-times associate-/r* associate-/r/ add-log-exp
3×flip3-+ pow-prod-down associate-*l/ prod-exp cbrt-unprod flip-+ associate-/l* unswap-sqr
2×cbrt-undiv sqrt-pow1 div-exp *-commutative div-inv difference-of-squares
1×distribute-rgt-in frac-2neg distribute-lft-in pow1/2 clear-num distribute-lft-out--
Counts
4 → 114
Calls
4 calls:
28.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
9.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
36.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
9.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)))
74.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
215.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
146.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))

simplify93.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
08231338
136071238
250021238

prune379.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
0.3b
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
9.9b
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×times-frac
25×*-un-lft-identity
24×associate-*l*
23×add-cube-cbrt
20×add-exp-log add-cbrt-cube
14×pow1
8×sqrt-prod
7×associate-*r/ prod-exp cbrt-unprod
6×sqrt-div associate-*l/
5×flip3-- pow-prod-down flip--
4×associate-*r* associate-/r* associate-/r/ add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×frac-times sqrt-pow1 *-commutative div-inv difference-of-squares unswap-sqr
1×frac-2neg pow1/2 clear-num distribute-lft-out--
Counts
4 → 111
Calls
4 calls:
7.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
36.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
10.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
109.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

series575.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
190.0ms
(* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand)
148.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
162.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))

simplify72.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
07541234
130421085
250021085

prune366.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 9.0 (- a (/ 1.0 3.0)))
0.1b
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.2b
(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
9.9b
(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×add-exp-log add-cbrt-cube
16×associate-*r*
15×*-un-lft-identity
11×pow1 add-cube-cbrt
10×times-frac
9×associate-*r/ associate-*l*
6×flip3-- sqrt-div prod-exp flip-- cbrt-unprod
4×cbrt-undiv div-exp associate-/r* sqrt-prod associate-/r/ add-log-exp difference-of-squares
3×pow-prod-down
2×distribute-rgt-in frac-times sub-neg distribute-lft-in sqrt-pow1 associate-*l/ *-commutative div-inv distribute-lft-out-- unswap-sqr
1×frac-2neg pow1/2 clear-num associate-/l*
Counts
4 → 102
Calls
4 calls:
25.0ms
(* 9.0 (- a (/ 1.0 3.0)))
7.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
10.0ms
(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
54.0ms
(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* 9.0 (- a (/ 1.0 3.0)))
76.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
192.0ms
(/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
163.0ms
(* (- a (/ 1.0 3.0)) (/ (* 1.0 rand) (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify76.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06971023
13246897
25001897

prune502.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
0.3b
(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
0.3b
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
0.3b
(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×times-frac
25×*-un-lft-identity
23×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
14×pow1
9×associate-*l/
8×associate-*r/ sqrt-prod
7×flip3-- associate-*l* prod-exp flip-- cbrt-unprod
6×sqrt-div
5×pow-prod-down
4×frac-times associate-/r* associate-/r/ add-log-exp
3×cbrt-undiv div-exp associate-/l*
2×sqrt-pow1 *-commutative div-inv difference-of-squares unswap-sqr
1×frac-2neg pow1/2 clear-num distribute-lft-out--
Counts
4 → 115
Calls
4 calls:
7.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
113.0ms
(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
11.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
52.0ms
(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (* 9.0 (- a (/ 1.0 3.0))))
167.0ms
(* (* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))) rand)
142.0ms
(/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0)))))
127.0ms
(* (- a (/ 1.0 3.0)) (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))))

simplify80.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07271338
132531177
250011177

prune352.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01913
11913

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.1s27843×body80nan
842.0ms9136×body80valid