Details

Time bar (total: 14.7s)

sample377.0ms

Algorithm
intervals
Results
48.0ms45×body1280valid
31.0ms47×body640valid
21.0ms152×body80valid
10.0ms22×body320valid
5.0ms47×body80nan
5.0ms15×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04215
18314
215114
335614
4106314
5500214

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (tan B))
0.2b
(* x (/ 1.0 (tan B)))
6.7b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.5b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite262.0ms

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:
6.0ms
(/ 1.0 (tan B))
18.0ms
(* x (/ 1.0 (tan B)))
174.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
58.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series551.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1.0 (tan B))
103.0ms
(* x (/ 1.0 (tan B)))
267.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
147.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify83.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07671428
131831338
250011337

prune980.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

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)))
0.2b
(* x (/ 1.0 (tan B)))
0.3b
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
19.5b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite365.0ms

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:
161.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
18.0ms
(* x (/ 1.0 (tan B)))
128.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
51.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series849.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
99.0ms
(* x (/ 1.0 (tan B)))
290.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
131.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify97.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
08482078
137401960
250021960

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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))
19.5b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite351.0ms

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:
10.0ms
(/ (* x 1.0) (tan B))
158.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
125.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
48.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series840.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (* x 1.0) (tan B))
324.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
287.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
128.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify85.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
08012023
134981905
250011905

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
0.3b
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
19.5b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite671.0ms

Algorithm
rewrite-expression-head
Rules
76×add-exp-log
34×prod-exp
30×add-sqr-sqrt
24×div-exp
23×add-cube-cbrt *-un-lft-identity times-frac
20×add-cbrt-cube
18×associate-*r*
16×pow-to-exp unpow-prod-down pow-exp
13×pow-unpow
7×pow1 associate-/l*
6×associate-*l* cbrt-unprod sqr-pow
4×cbrt-undiv add-log-exp unswap-sqr
3×div-inv
2×*-commutative
1×pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r*
Counts
4 → 132
Calls
4 calls:
158.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
290.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
167.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
50.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
232.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
333.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
321.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
123.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06821811
129041481
250011437

prune837.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes285.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.9b

bsearch261.0ms

Steps
ItersRangePoint
10
0.6595217963696074
11346062936.778234
33048172.790577427
3
-8.124316099194928e+31
-6.9013391252891795e+31
-7.890396061883058e+31

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05941
16741
26741

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s1676×body1280valid
950.0ms1436×body640valid
689.0ms4772×body80valid
315.0ms695×body320valid
190.0ms1645×body80nan
102.0ms331×body160valid