Details

Time bar (total: 11.7s)

sample82.0ms

Algorithm
intervals
Results
26.0ms81×body1280valid
20.0ms75×body640valid
14.0ms277×body80valid
5.0ms33×body320valid
2.0ms15×body160valid

simplify21.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b
(/ (cos th) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
70×add-sqr-sqrt
60×add-cube-cbrt *-un-lft-identity
44×associate-*l* sqrt-prod
32×add-exp-log add-cbrt-cube
14×pow1
12×prod-exp associate-/r* cbrt-unprod
6×cbrt-undiv div-exp pow-prod-down associate-/l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg associate-*r* associate-*l/ clear-num *-commutative
Counts
4 → 176
Calls
4 calls:
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
20.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series371.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
123.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
60.0ms
(/ (cos th) (sqrt 2.0))
69.0ms
(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05101324
120211196
250021174

prune539.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b
(/ (pow a2 2) (sqrt 2.0))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
142×times-frac
121×add-sqr-sqrt
94×add-cube-cbrt *-un-lft-identity
77×sqrt-prod
53×associate-*r*
41×unpow-prod-down
33×add-exp-log
25×associate-*l* add-cbrt-cube
15×unpow2 sqr-pow
12×associate-/r* unswap-sqr
11×pow1 associate-/l*
10×prod-exp
9×div-exp
8×cbrt-unprod
5×cbrt-undiv
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv add-log-exp
2×pow-to-exp frac-2neg pow-exp clear-num *-commutative
1×associate-*r/ associate-*l/
Counts
4 → 248
Calls
4 calls:
27.0ms
(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms
(/ (pow a2 2) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series364.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
113.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
67.0ms
(/ (pow a2 2) (sqrt 2.0))
60.0ms
(/ (cos th) (sqrt 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
07021826
130341592
250021579

prune660.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.3b
(/ (pow a2 2) (sqrt 2.0))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
1167×times-frac
1164×sqrt-prod
643×add-sqr-sqrt
609×add-cube-cbrt *-un-lft-identity
283×associate-*l*
42×associate-/l*
37×add-exp-log
34×add-cbrt-cube
24×associate-/r*
23×div-inv
21×unpow-prod-down
13×div-exp unswap-sqr
11×cbrt-undiv
9×pow1 prod-exp cbrt-unprod
7×unpow2 sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg pow-prod-down clear-num
1×pow-to-exp associate-*r* associate-*l/ pow-exp *-commutative associate-/l/
Counts
4 → 789
Calls
4 calls:
102.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
6.0ms
(/ (pow a2 2) (sqrt 2.0))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series566.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
66.0ms
(/ (pow a2 2) (sqrt 2.0))
276.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
108.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify115.0ms

Algorithm
egg-herbie
Counts
801 → 801
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0165910223
150019003

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow a2 2) (sqrt 2.0))
0.3b
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
1546×times-frac sqrt-prod
855×add-sqr-sqrt
798×*-un-lft-identity
786×add-cube-cbrt
392×cbrt-prod
376×associate-*l*
57×add-exp-log
42×associate-/l*
34×add-cbrt-cube
29×div-inv unswap-sqr
27×associate-/r*
23×div-exp
21×unpow-prod-down
15×prod-exp
13×pow1
11×cbrt-undiv
9×cbrt-unprod
7×pow-flip sqrt-pow1 unpow2 sqr-pow
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg pow1/2 pow-prod-down clear-num
2×pow1/3 pow-div
1×pow-to-exp associate-*r* associate-*l/ pow-exp *-commutative associate-/l/ inv-pow
Counts
4 → 1010
Calls
4 calls:
5.0ms
(/ (pow a2 2) (sqrt 2.0))
132.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
24.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
5.0ms
(/ 1 (sqrt (sqrt 2.0)))

series438.0ms

Counts
4 → 8
Calls
4 calls:
67.0ms
(/ (pow a2 2) (sqrt 2.0))
371.0ms
(* (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0)))) (* a1 a1))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (cbrt (sqrt 2.0))))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify146.0ms

Algorithm
egg-herbie
Counts
1018 → 1018
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0192213471
1500112580

prune3.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes327.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02924
12924

end0.0ms

sample2.2s

Algorithm
intervals
Results
818.0ms2488×body1280valid
459.0ms2085×body640valid
398.0ms7982×body80valid
164.0ms1075×body320valid
51.0ms489×body160valid