Details

Time bar (total: 12.0s)

sample376.0ms

Algorithm
intervals
Results
44.0ms44×body1280valid
29.0ms43×body640valid
21.0ms156×body80valid
11.0ms25×body320valid
6.0ms56×body80nan
3.0ms11×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
04315
19114
216914
337814
4110014
5500114

prune11.0ms

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)))
7.3b
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
18.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
37×times-frac
36×add-cube-cbrt *-un-lft-identity
30×pow-unpow
14×associate-*r*
13×distribute-lft-neg-in distribute-rgt-neg-in
12×add-exp-log
11×add-cbrt-cube
7×pow1
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×unpow-prod-down associate-*l* associate-/r* associate-/l*
2×tan-quot cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×neg-sub0 pow-to-exp pow-neg neg-mul-1 pow-pow frac-2neg associate-*r/ pow-prod-down pow-exp clear-num *-commutative fma-udef pow-sub sqr-pow
Counts
4 → 123
Calls
4 calls:
2.0ms
(/ 1.0 (tan B))
8.0ms
(* x (/ 1.0 (tan B)))
0.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
26.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series540.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1.0 (tan B))
109.0ms
(* x (/ 1.0 (tan B)))
232.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
163.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06281028
12518940
25001937

prune597.0ms

Filtered
135 candidates to 112 candidates (83.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ F (sin B))
0.1b
(/ (* x 1.0) (tan B))
7.3b
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
18.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity times-frac
13×distribute-lft-neg-in distribute-rgt-neg-in
12×add-exp-log
11×add-cbrt-cube
6×associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
3×cbrt-undiv unpow-prod-down div-exp
2×frac-2neg clear-num
1×tan-quot neg-sub0 pow-to-exp pow-neg neg-mul-1 pow-pow pow-exp prod-exp associate-/r/ cbrt-unprod fma-udef pow-sub sqr-pow
Counts
4 → 111
Calls
4 calls:
2.0ms
(/ F (sin B))
4.0ms
(/ (* x 1.0) (tan B))
0.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
26.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series527.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ F (sin B))
107.0ms
(/ (* x 1.0) (tan B))
222.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (/ (* x 1.0) (tan B))))
147.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0616964
12352876
25001873

prune508.0ms

Filtered
123 candidates to 100 candidates (81.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ F (sin B))
0.2b
(* (/ (* x 1.0) (sin B)) (cos B))
7.3b
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
18.3b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
30×pow-unpow times-frac
16×add-exp-log
15×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
7×pow1 associate-*l*
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv unpow-prod-down div-exp associate-*r* associate-/r* associate-/l*
1×neg-sub0 pow-to-exp pow-neg neg-mul-1 pow-pow frac-2neg pow-prod-down associate-*l/ pow-exp clear-num *-commutative fma-udef pow-sub unswap-sqr sqr-pow
Counts
4 → 116
Calls
4 calls:
2.0ms
(/ F (sin B))
10.0ms
(* (/ (* x 1.0) (sin B)) (cos B))
0.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
24.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ F (sin B))
101.0ms
(* (/ (* x 1.0) (sin B)) (cos B))
212.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* (/ (* x 1.0) (sin B)) (cos B))))
147.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06701083
12594968
25002965

prune507.0ms

Filtered
128 candidates to 100 candidates (78.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
7.3b
(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (/ (* x 1.0) (tan B))))
18.8b
(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
18.8b
(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
188×pow-unpow
178×add-sqr-sqrt
166×add-cube-cbrt *-un-lft-identity
78×distribute-lft-neg-in distribute-rgt-neg-in
24×unpow-prod-down
18×add-exp-log
14×div-inv
12×sqr-pow
9×pow-neg distribute-frac-neg prod-exp unswap-sqr
8×neg-sub0 pow-to-exp div-sub pow-exp pow-sub
7×swap-sqr associate-*r* associate-*l*
6×pow1 neg-mul-1 add-cbrt-cube
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp
2×pow-pow associate-*r/ associate-*l/
1×pow2 pow-prod-down pow-sqr un-div-inv *-commutative pow-prod-up cbrt-unprod fma-udef
Counts
4 → 297
Calls
4 calls:
10.0ms
(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
0.0ms
(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (/ (* x 1.0) (tan B))))
10.0ms
(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
10.0ms
(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
866.0ms
(* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)))
249.0ms
(fma (/ F (sin B)) (* (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (/ (* x 1.0) (tan B))))
311.0ms
(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))
313.0ms
(pow (fma x 2.0 (fma F F 2.0)) (/ (- (/ 1.0 2.0)) 2))

simplify118.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
012343275
144793077
250023052

prune1.5s

Filtered
309 candidates to 244 candidates (79.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch294.0ms

Steps
ItersRangePoint
9
489495.903442394
13630805831702.373
125389888783.81546
8
-3.648591357906051e+92
-3.3469565555295054e+88
-4.7370863933049426e+91

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05039
15539
25539

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s1676×body1280valid
881.0ms1353×body640valid
663.0ms4838×body80valid
303.0ms693×body320valid
165.0ms1629×body80nan
98.0ms329×body160valid