Details

Time bar (total: 10.2s)

analyze2.0s (19.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%93.6%6.4%8
9.4%84.3%6.4%9
14.8%75.7%9.5%10
16%71.4%12.6%11
20.9%65.7%13.4%12
24.2%60.5%15.3%13
24.8%58.6%16.6%14

sample136.0ms (1.3%)

Algorithm
1×intervals
Results
52.0ms54×body1280valid
24.0ms38×body640valid
18.0ms122×body80valid
12.0ms26×body320valid
5.0ms16×body160valid
4.0ms23×body80invalid
1.0ms5×body80nan

simplify467.0ms (4.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0495126
1495126

prune17.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 10.2b

Counts
2 → 2

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
0.3b
(* x (/ 1.0 (tan B)))
0.4b
(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
16.1b
(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))

rewrite52.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
85×times-frac
79×add-sqr-sqrt
64×add-cube-cbrt *-un-lft-identity
39×associate-*r*
34×pow-unpow
25×add-exp-log unpow-prod-down
16×add-cbrt-cube
9×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqr-pow
7×div-exp associate-/l*
6×associate-*l* prod-exp unswap-sqr
4×cbrt-unprod div-inv add-log-exp
3×cbrt-undiv pow-to-exp neg-mul-1 pow-exp associate-/r*
2×neg-sub0 pow-neg div-sub associate-*r/ distribute-frac-neg pow-prod-down *-commutative associate-/l/ pow-sub
1×tan-quot pow-pow frac-2neg clear-num associate-/r/
Counts
4 → 178
Calls

4 calls:

14.0ms
(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
13.0ms
(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))
10.0ms
(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
7.0ms
(* x (/ 1.0 (tan B)))

series247.0ms (2.4%)

Counts
4 → 12
Calls

4 calls:

94.0ms
(* F (/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B)))
94.0ms
(/ (pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0)) (sin B))
32.0ms
(pow (+ (* F F) (+ 2.0 (* x 2.0))) (/ (neg 1.0) 2.0))
27.0ms
(* x (/ 1.0 (tan B)))

simplify75.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049573681
149573681

prune631.0ms (6.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New17515190
Fresh101
Picked101
Done000
Total17715192

Merged error: 9.9b

Counts
192 → 15

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
0.3b
(* x (/ 1.0 (tan B)))
0.4b
(* (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (/ 1 (sin B)))
16.1b
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

rewrite48.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
59×add-exp-log
53×add-sqr-sqrt
49×times-frac
43×add-cube-cbrt *-un-lft-identity
34×pow-unpow associate-*r*
33×prod-exp
23×add-cbrt-cube
9×pow1 distribute-lft-neg-in distribute-rgt-neg-in div-exp cbrt-unprod
8×associate-*r/
7×pow-neg unpow-prod-down distribute-frac-neg associate-*l*
6×pow-to-exp pow-exp
5×unswap-sqr
4×neg-sub0 rec-exp 1-exp div-sub un-div-inv pow-sub add-log-exp
3×cbrt-undiv frac-times neg-mul-1 associate-*l/ *-commutative div-inv sqr-pow
2×pow-prod-down
1×tan-quot pow-pow associate-/r/
Counts
4 → 162
Calls

4 calls:

14.0ms
(* (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (/ 1 (sin B)))
12.0ms
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))
10.0ms
(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
7.0ms
(* x (/ 1.0 (tan B)))

series206.0ms (2%)

Counts
4 → 12
Calls

4 calls:

93.0ms
(* (* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))) (/ 1 (sin B)))
68.0ms
(* F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0)))
22.0ms
(* x (/ 1.0 (tan B)))
21.0ms
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ (neg 1.0) 2.0))

simplify68.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049422797
149422797

prune487.0ms (4.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1713174
Fresh21214
Picked101
Done000
Total17415189

Merged error: 9.9b

Counts
189 → 15

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
0.3b
(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
0.3b
(* x (/ 1.0 (tan B)))
16.1b
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite37.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
35×add-sqr-sqrt
25×add-exp-log add-cube-cbrt *-un-lft-identity
22×times-frac
17×associate-*r*
16×add-cbrt-cube
13×pow-unpow
10×associate-*l*
8×prod-exp
7×pow1 unpow-prod-down
5×div-exp unswap-sqr
4×cbrt-unprod add-log-exp
3×cbrt-undiv pow-to-exp pow-exp div-inv associate-/l* sqr-pow
2×*-commutative
1×tan-quot pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r* associate-/r/
Counts
4 → 108
Calls

4 calls:

10.0ms
(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
10.0ms
(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
7.0ms
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))
7.0ms
(* x (/ 1.0 (tan B)))

series201.0ms (2%)

Counts
4 → 12
Calls

4 calls:

92.0ms
(/ F (* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B)))
65.0ms
(* (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)) (sin B))
23.0ms
(* x (/ 1.0 (tan B)))
21.0ms
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify66.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
050661891

prune342.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New11010120
Fresh10414
Picked101
Done000
Total12114135

Merged error: 9.9b

Counts
135 → 14

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
0.3b
(* x (/ 1.0 (tan B)))
0.4b
(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
16.1b
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

rewrite48.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
199×times-frac
123×add-sqr-sqrt
118×add-cube-cbrt *-un-lft-identity
51×unpow-prod-down
28×associate-/l*
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
14×associate-*r*
13×pow-unpow
11×div-exp
10×associate-/r*
8×div-inv
7×pow1
5×cbrt-undiv
4×add-log-exp
3×pow-to-exp associate-*l* pow-exp
2×frac-2neg prod-exp clear-num cbrt-unprod unswap-sqr
1×tan-quot pow-pow associate-*r/ pow-prod-down associate-/r/ *-commutative associate-/l/
Counts
4 → 225
Calls

4 calls:

15.0ms
(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
8.0ms
(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
8.0ms
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))
7.0ms
(* x (/ 1.0 (tan B)))

series207.0ms (2%)

Counts
4 → 12
Calls

4 calls:

94.0ms
(/ (/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))) (sin B))
67.0ms
(/ F (pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0)))
24.0ms
(* x (/ 1.0 (tan B)))
21.0ms
(pow (+ (* F F) (+ 2.0 (* 2.0 x))) (/ 1.0 2.0))

simplify76.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
050545954

prune666.0ms (6.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New2361237
Fresh11213
Picked011
Done000
Total23714251

Merged error: 9.9b

Counts
251 → 14

regimes345.0ms (3.4%)

Accuracy

Total 0.3b remaining (3.3%)

Threshold costs 0.3b (3.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05525
15525

end0.0ms (0%)

sample3.7s (36.1%)

Algorithm
1×intervals
Results
1.5s1623×body1280valid
825.0ms1333×body640valid
574.0ms3980×body80valid
297.0ms690×body320valid
109.0ms374×body160valid
103.0ms709×body80invalid
13.0ms126×body80nan

Profiling

Loading profile data...