Details

Time bar (total: 12.6s)

sample390.0ms

Algorithm
intervals
Results
46.0ms44×body1280valid
30.0ms43×body640valid
22.0ms156×body80valid
11.0ms25×body320valid
6.0ms56×body80nan
3.0ms11×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04215
18314
215114
335614
4106314
5500214

prune25.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (tan B))
0.3b
(* x (/ 1.0 (tan B)))
7.5b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite135.0ms

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)))
89.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
28.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series614.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1.0 (tan B))
116.0ms
(* x (/ 1.0 (tan B)))
298.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
163.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify86.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07671428
131831338
250011337

prune641.0ms

Filtered
167 candidates to 129 candidates (77.2%)
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
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b
(* x (/ 1.0 (tan B)))
0.3b
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
18.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite187.0ms

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:
84.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
9.0ms
(* x (/ 1.0 (tan B)))
63.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
25.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series939.0ms

Counts
4 → 12
Calls
4 calls:
349.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
111.0ms
(* x (/ 1.0 (tan B)))
329.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
150.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify94.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
08482078
137401960
250021960

prune672.0ms

Filtered
186 candidates to 143 candidates (76.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* x 1.0) (tan B))
0.2b
(* 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))
18.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite180.0ms

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))
83.0ms
(* 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))
25.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series944.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ (* x 1.0) (tan B))
358.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
319.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
150.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify89.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
08012023
134981905
250011905

prune670.0ms

Filtered
175 candidates to 137 candidates (78.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
0.2b
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b
(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
18.2b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite271.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
34×prod-exp
27×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity add-cbrt-cube
16×div-exp
15×times-frac
14×associate-*r*
13×pow-unpow
8×pow1 pow-to-exp rec-exp 1-exp pow-exp
7×unpow-prod-down
6×associate-*l* cbrt-unprod
4×cbrt-undiv add-log-exp unswap-sqr
3×div-inv associate-/l* sqr-pow
2×*-commutative
1×pow-flip pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r* un-div-inv inv-pow
Counts
4 → 123
Calls
4 calls:
121.0ms
(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
78.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
42.0ms
(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
25.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
310.0ms
(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
258.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
765.0ms
(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
140.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify83.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06361469
129121293
250021283

prune375.0ms

Filtered
135 candidates to 82 candidates (60.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch295.0ms

Steps
ItersRangePoint
9
489495.903442394
13630805831702.373
22462302.130518436
8
-3.064295880915072e+83
-6.361978161628334e+80
-7.766754916751145e+80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04638
14638

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s1676×body1280valid
877.0ms1353×body640valid
674.0ms4838×body80valid
312.0ms693×body320valid
164.0ms1629×body80nan
101.0ms329×body160valid