Details

Time bar (total: 11.0s)

sample373.0ms

Algorithm
intervals
Results
49.0ms57×body1280valid
24.0ms41×body640valid
20.0ms149×body80valid
10.0ms26×body320valid
5.0ms55×body80nan
3.0ms11×body160valid

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04315
19114
216914
337814
4110014
5500114

prune26.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 13.7b

Counts
2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (+ (* F F) 2.0) (* 2.0 x))
0.2b
(* x (/ 1.0 (tan B)))
5.9b
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
20.9b
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
30×pow-unpow
29×add-cube-cbrt *-un-lft-identity
28×times-frac
14×associate-*r*
13×distribute-lft-neg-in distribute-rgt-neg-in
10×add-exp-log
9×add-cbrt-cube add-log-exp
7×pow1
4×expm1-log1p-u log1p-expm1-u
3×unpow-prod-down fma-def associate-*l* sum-log div-inv
2×prod-exp cbrt-unprod unswap-sqr
1×tan-quot cbrt-undiv +-commutative neg-sub0 pow-to-exp pow-neg neg-mul-1 associate-+l+ pow-pow flip3-+ associate-*r/ div-exp pow-prod-down pow-exp associate-/r/ *-commutative flip-+ fma-udef pow-sub sqr-pow
Counts
4 → 111
Calls
4 calls:
7.0ms
(+ (+ (* F F) 2.0) (* 2.0 x))
7.0ms
(* x (/ 1.0 (tan B)))
1.0ms
(fma (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (- (* x (/ 1.0 (tan B)))))
12.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series515.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ (+ (* F F) 2.0) (* 2.0 x))
111.0ms
(* 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)))))
158.0ms
(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify72.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
0676980
12827879
25001875

prune525.0ms

Filtered
123 candidates to 101 candidates (82.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10914123
Fresh000
Picked101
Done000
Total11014124

Merged error: 0.0b

Counts
124 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)))
5.9b
(fma (/ F (sin B)) (* (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (* x (/ 1.0 (tan B)))))
21.4b
(pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))
21.4b
(pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))

rewrite53.0ms

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:
8.0ms
(* (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)))
1.0ms
(fma (/ F (sin B)) (* (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (* x (/ 1.0 (tan B)))))
14.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))
11.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
720.0ms
(* (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)))
251.0ms
(fma (/ F (sin B)) (* (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2)) (pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))) (- (* x (/ 1.0 (tan B)))))
140.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))
147.0ms
(pow (fma F F (fma 2.0 x 2.0)) (/ (- (/ 1.0 2.0)) 2))

simplify109.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
011523168
141222956
250022927

prune1.4s

Filtered
309 candidates to 244 candidates (79.0%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New3081309
Fresh11213
Picked011
Done000
Total30914323

Merged error: 0.0b

Counts
323 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1.0 (tan B)))
0.3b
(fma F F (fma 2.0 x 2.0))
0.4b
(/ (* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F) (sin B))
20.9b
(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
31×times-frac
30×add-cube-cbrt pow-unpow *-un-lft-identity
20×add-exp-log
14×associate-*r* add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
7×pow1
5×div-exp prod-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv unpow-prod-down associate-*l* associate-/r* cbrt-unprod
2×neg-sub0 pow-to-exp pow-neg associate-*l/ pow-exp associate-/l/ pow-sub unswap-sqr
1×tan-quot neg-mul-1 pow-pow frac-2neg associate-*r/ pow-prod-down clear-num associate-/r/ *-commutative fma-udef associate-/l* sqr-pow
Counts
4 → 120
Calls
4 calls:
7.0ms
(* x (/ 1.0 (tan B)))
1.0ms
(fma F F (fma 2.0 x 2.0))
9.0ms
(/ (* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F) (sin B))
5.0ms
(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

series658.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* x (/ 1.0 (tan B)))
29.0ms
(fma F F (fma 2.0 x 2.0))
369.0ms
(/ (* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F) (sin B))
150.0ms
(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0675898
12850818
25002816

prune505.0ms

Filtered
132 candidates to 104 candidates (78.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1257132
Fresh8412
Picked101
Done011
Total13412146

Merged error: 0.0b

Counts
146 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F)
0.3b
(fma F F (fma 2.0 x 2.0))
0.4b
(/ (* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F) (sin B))
20.9b
(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt pow-unpow
25×add-cube-cbrt *-un-lft-identity
21×times-frac
20×add-exp-log
13×distribute-lft-neg-in distribute-rgt-neg-in
11×add-cbrt-cube
7×unpow-prod-down associate-*l*
6×prod-exp
5×pow1
4×expm1-log1p-u div-exp associate-*l/ log1p-expm1-u add-log-exp
3×neg-sub0 pow-to-exp pow-neg associate-*r* pow-exp associate-/r* div-inv pow-sub unswap-sqr sqr-pow
2×cbrt-undiv cbrt-unprod associate-/l/
1×neg-mul-1 pow-pow frac-2neg clear-num *-commutative fma-udef associate-/l*
Counts
4 → 114
Calls
4 calls:
5.0ms
(* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F)
1.0ms
(fma F F (fma 2.0 x 2.0))
6.0ms
(/ (* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F) (sin B))
5.0ms
(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

series758.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F)
35.0ms
(fma F F (fma 2.0 x 2.0))
357.0ms
(/ (* (pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0))) F) (sin B))
153.0ms
(pow (fma F F (fma 2.0 x 2.0)) (- (/ 1.0 2.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0564967
12399884
25002881

prune425.0ms

Filtered
126 candidates to 100 candidates (79.4%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1233126
Fresh3710
Picked101
Done011
Total12711138

Merged error: 0.0b

Counts
138 → 11

regimes181.0ms

Accuracy

97.4% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.7b

bsearch226.0ms

Steps
ItersRangePoint
10
0.000608309806168642
2529654550.545884
50548945.160980105
5
-1.759228136062667e+159
-8.428741314088731e+158
-8.503058033323655e+158

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04032
14632
24632

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.3s1624×body1280valid
790.0ms1435×body640valid
586.0ms4792×body80valid
258.0ms694×body320valid
148.0ms1609×body80nan
92.0ms368×body160valid