Details

Time bar (total: 12.2s)

sample390.0ms

Algorithm
intervals
Results
59.0ms60×body1280valid
24.0ms38×body640valid
23.0ms157×body80valid
7.0ms17×body320valid
7.0ms58×body80nan
4.0ms14×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04215
18314
215114
335614
4106314
5500214

prune24.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (tan B))
0.2b
(* x (/ 1.0 (tan B)))
8.6b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.7b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
49×times-frac
45×add-cube-cbrt *-un-lft-identity
30×pow-unpow
25×add-exp-log
21×associate-*r*
16×associate-*l* add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
8×unpow-prod-down prod-exp unswap-sqr
7×pow1
5×div-exp div-inv
4×pow-neg cbrt-unprod add-log-exp sqr-pow
3×cbrt-undiv neg-sub0 pow-to-exp associate-*r/ pow-exp associate-/r* associate-/l* pow-sub
2×tan-quot frac-times associate-/r/ *-commutative
1×neg-mul-1 pow-pow frac-2neg pow-prod-down associate-*l/ clear-num un-div-inv
Counts
4 → 155
Calls
4 calls:
2.0ms
(/ 1.0 (tan B))
9.0ms
(* x (/ 1.0 (tan B)))
87.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
27.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series581.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ 1.0 (tan B))
110.0ms
(* x (/ 1.0 (tan B)))
283.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
155.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify82.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07671428
131831338
250011337

prune633.0ms

Filtered
167 candidates to 129 candidates (77.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1.0 (tan B)))
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))
17.7b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
73×times-frac
59×add-cube-cbrt *-un-lft-identity
39×associate-*r*
30×pow-unpow
25×add-exp-log unpow-prod-down
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
9×pow1 sqr-pow
7×div-exp associate-/l*
6×associate-*l* prod-exp unswap-sqr
5×div-inv
4×cbrt-unprod add-log-exp
3×cbrt-undiv pow-to-exp pow-exp associate-/r*
2×neg-sub0 pow-neg associate-*r/ pow-prod-down *-commutative associate-/l/ pow-sub
1×tan-quot neg-mul-1 pow-pow frac-2neg clear-num associate-/r/
Counts
4 → 174
Calls
4 calls:
8.0ms
(* x (/ 1.0 (tan B)))
82.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
62.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
26.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series895.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* x (/ 1.0 (tan B)))
342.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
307.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
139.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify101.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
08482078
137401960
250021960

prune694.0ms

Filtered
186 candidates to 143 candidates (76.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* x 1.0) (tan B))
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))
17.7b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
63×add-sqr-sqrt
53×add-cube-cbrt *-un-lft-identity
30×pow-unpow
25×add-exp-log unpow-prod-down associate-*r*
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
9×sqr-pow
8×div-exp associate-/l*
7×pow1
6×associate-/r*
5×prod-exp div-inv
4×cbrt-undiv add-log-exp unswap-sqr
3×pow-to-exp associate-*l* pow-exp cbrt-unprod
2×neg-sub0 pow-neg frac-2neg clear-num associate-/l/ pow-sub
1×tan-quot neg-mul-1 pow-pow associate-*r/ pow-prod-down associate-/r/ *-commutative
Counts
4 → 163
Calls
4 calls:
4.0ms
(/ (* x 1.0) (tan B))
81.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
61.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
24.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series901.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (* x 1.0) (tan B))
344.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
311.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
139.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify93.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
08012023
134981905
250011905

prune650.0ms

Filtered
175 candidates to 136 candidates (77.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (* x 1.0) (sin B)) (cos B))
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))
17.7b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt times-frac
54×add-cube-cbrt *-un-lft-identity
30×pow-unpow
29×add-exp-log
28×associate-*r*
25×unpow-prod-down
20×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-*l*
9×pow1 sqr-pow
8×div-exp prod-exp
7×associate-/l*
6×cbrt-unprod
5×div-inv unswap-sqr
4×cbrt-undiv add-log-exp
3×pow-to-exp pow-exp associate-/r*
2×neg-sub0 pow-neg pow-prod-down *-commutative associate-/l/ pow-sub
1×neg-mul-1 pow-pow frac-2neg associate-*r/ associate-*l/ clear-num
Counts
4 → 168
Calls
4 calls:
10.0ms
(* (/ (* x 1.0) (sin B)) (cos B))
81.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
61.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
24.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series924.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (/ (* x 1.0) (sin B)) (cos B))
355.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
320.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
146.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify95.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
08522114
137221973
250011973

prune651.0ms

Filtered
180 candidates to 137 candidates (76.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes190.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.9b

bsearch255.0ms

Steps
ItersRangePoint
8
11257.791762216355
390892005.0771458
17231.894334771598
7
-2595256309730746.0
-118859067955370.34
-120085968004636.11

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06243
17043
27043

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.8s1789×body1280valid
867.0ms1341×body640valid
654.0ms4718×body80valid
301.0ms686×body320valid
180.0ms1667×body80nan
94.0ms326×body160valid