Details

Time bar (total: 13.5s)

sample480.0ms

Algorithm
intervals
Results
61.0ms59×body640valid
53.0ms51×body1280valid
21.0ms145×body80valid
7.0ms50×body80nan
6.0ms15×body320valid
4.0ms14×body160valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
04215
18314
215114
335614
4106314
5500214

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (tan B))
0.3b
(* x (/ 1.0 (tan B)))
7.3b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.6b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite266.0ms

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)))
175.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
60.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1.0 (tan B))
105.0ms
(* x (/ 1.0 (tan B)))
275.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
151.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify81.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07671428
131831338
250011337

prune664.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))
17.6b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite371.0ms

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:
166.0ms
(* 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))
52.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series861.0ms

Counts
4 → 12
Calls
4 calls:
328.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
103.0ms
(* x (/ 1.0 (tan B)))
298.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
132.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify97.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
08482078
137421960
250011960

prune719.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))
17.6b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite359.0ms

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:
12.0ms
(/ (* x 1.0) (tan B))
163.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
127.0ms
(/ (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)))

series860.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (* x 1.0) (tan B))
327.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
299.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
132.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify91.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
08012023
134981905
250011905

prune685.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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)))
0.3b
(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
17.5b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite570.0ms

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:
258.0ms
(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
161.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
94.0ms
(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
51.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
283.0ms
(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
232.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
732.0ms
(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
124.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06361469
129121293
250021283

prune390.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes215.0ms

Accuracy

97.4% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.2b

bsearch286.0ms

Steps
ItersRangePoint
9
2.0513987020488157e-07
98.28323543872592
96.48230808888776
8
-6600684023240.848
-1557293340.659962
-2230687376.113047

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06242
16942
26942

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s1626×body1280valid
947.0ms1419×body640valid
689.0ms4741×body80valid
333.0ms703×body320valid
181.0ms1688×body80nan
106.0ms347×body160valid