Details

Time bar (total: 12.4s)

sample401.0ms

Algorithm
intervals
Results
60.0ms57×body1280valid
29.0ms41×body640valid
28.0ms149×body80valid
12.0ms26×body320valid
7.0ms55×body80nan
5.0ms11×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04215
18314
215114
335614
4106314
5500214

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b
(* x (/ 1.0 (tan B)))
6.0b
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
20.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
40×times-frac
37×add-cube-cbrt *-un-lft-identity
30×pow-unpow
23×add-exp-log
21×associate-*r*
16×associate-*l*
14×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
9×add-log-exp
8×unpow-prod-down prod-exp unswap-sqr
7×pow1
4×pow-neg div-exp cbrt-unprod div-inv sqr-pow
3×neg-sub0 pow-to-exp associate-*r/ pow-exp sum-log pow-sub
2×cbrt-undiv frac-times *-commutative
1×tan-quot +-commutative neg-mul-1 associate-+l+ pow-pow flip3-+ pow-prod-down associate-*l/ associate-/r/ un-div-inv flip-+
Counts
4 → 140
Calls
4 calls:
16.0ms
(+ (+ (* F F) 2.0) (* 2.0 x))
8.0ms
(* x (/ 1.0 (tan B)))
85.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
26.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (* F F) 2.0) (* 2.0 x))
110.0ms
(* x (/ 1.0 (tan B)))
295.0ms
(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
153.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify88.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08131382
134951293
250011292

prune589.0ms

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)))
0.2b
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.4b
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
20.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite182.0ms

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)))
81.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
58.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
27.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series923.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* x (/ 1.0 (tan B)))
350.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
323.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
142.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify95.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
08482078
137401960
250021960

prune707.0ms

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
(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.4b
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
20.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
63×times-frac
61×add-sqr-sqrt
51×add-cube-cbrt *-un-lft-identity
30×pow-unpow
25×unpow-prod-down associate-*r*
20×add-exp-log
13×distribute-lft-neg-in distribute-rgt-neg-in
11×add-cbrt-cube
9×add-log-exp sqr-pow
7×pow1 associate-/l*
6×div-exp
4×prod-exp div-inv unswap-sqr
3×pow-to-exp associate-*l* pow-exp associate-/r* sum-log
2×cbrt-undiv neg-sub0 pow-neg cbrt-unprod associate-/l/ pow-sub
1×+-commutative neg-mul-1 associate-+l+ pow-pow frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num *-commutative flip-+
Counts
4 → 154
Calls
4 calls:
16.0ms
(+ (+ (* F F) 2.0) (* 2.0 x))
79.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
57.0ms
(/ (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)))

series834.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (* F F) 2.0) (* 2.0 x))
350.0ms
(* 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))
141.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify91.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
07572000
133131894
250011894

prune646.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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
(* (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))))
20.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite311.0ms

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:
134.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
74.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
77.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
21.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
364.0ms
(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
249.0ms
(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
345.0ms
(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
136.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06831835
129051481
250021437

prune456.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes219.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.8b

bsearch289.0ms

Steps
ItersRangePoint
10
0.000608309806168642
2529654550.545884
69713870.93548934
7
-3401315516.193776
-51330663.2772825
-143202766.45461348

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04942
14942

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s1624×body1280valid
963.0ms1435×body640valid
788.0ms4792×body80valid
328.0ms694×body320valid
202.0ms1609×body80nan
118.0ms368×body160valid