Details

Time bar (total: 45.7s)

sample964.0ms

Algorithm
intervals
Results
641.0ms34×body320valid
97.0ms48×body1280valid
51.0ms34×body640valid
46.0ms154×body80valid
16.0ms57×body80nan
11.0ms16×body160valid

simplify3.1s

Counts
1 → 1
Iterations
IterNodes
done5001
62738
5849
4325
3161
290
143
020

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize90.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b
(* (/ 1.0 (tan B)) x)
0.3b
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
15.4b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
214×times-frac
133×add-sqr-sqrt
128×*-un-lft-identity add-cube-cbrt
51×unpow-prod-down
34×associate-/r*
30×pow-unpow
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
14×associate-*l*
13×distribute-lft-neg-in distribute-rgt-neg-in
12×associate-/r/
11×div-exp
9×div-inv
7×pow1
6×neg-sub0 pow-neg associate-/l* pow-sub
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp associate-*r* pow-exp
2×clear-num frac-2neg prod-exp cbrt-unprod unswap-sqr
1×neg-mul-1 pow-pow pow-prod-down associate-*l/ tan-quot *-commutative
Counts
4 → 262
Calls
4 calls:
12.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
15.0ms
(* (/ 1.0 (tan B)) x)
10.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
15.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
407.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
142.0ms
(* (/ 1.0 (tan B)) x)
326.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
242.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.8s

Counts
274 → 274
Iterations
IterNodes
done5004
24220
11302
0497

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 x) (tan B))
0.2b
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
0.3b
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
15.4b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
122×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
51×unpow-prod-down
37×associate-/r*
30×pow-unpow
25×add-exp-log
17×sqr-pow
16×add-cbrt-cube
13×distribute-lft-neg-in distribute-rgt-neg-in
12×div-exp associate-/r/
9×div-inv
7×associate-/l*
6×neg-sub0 cbrt-undiv pow-neg pow-sub
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp clear-num frac-2neg pow-exp
1×neg-mul-1 pow-pow prod-exp tan-quot cbrt-unprod
Counts
4 → 251
Calls
4 calls:
24.0ms
(/ (* 1.0 x) (tan B))
22.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
16.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
11.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (* 1.0 x) (tan B))
478.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
336.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
210.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.7s

Counts
263 → 263
Iterations
IterNodes
done5001
24316
11302
0481

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 x) (tan B))
0.2b
(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
0.4b
(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
15.4b
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
80×times-frac
59×add-exp-log
55×*-un-lft-identity
51×add-cube-cbrt
27×unpow-prod-down
25×div-exp associate-*r*
23×add-cbrt-cube
17×prod-exp
13×pow-unpow associate-*l*
12×unswap-sqr
11×sqr-pow
10×associate-/r*
7×pow1 cbrt-undiv
6×pow-to-exp pow-exp
5×cbrt-unprod div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u associate-/l* add-log-exp
2×clear-num frac-2neg
1×frac-times pow-pow pow-prod-down associate-*l/ tan-quot associate-*r/ associate-/r/ *-commutative
Counts
4 → 184
Calls
4 calls:
12.0ms
(/ (* 1.0 x) (tan B))
12.0ms
(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
39.0ms
(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
5.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
184.0ms
(/ (* 1.0 x) (tan B))
424.0ms
(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
551.0ms
(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
213.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.8s

Counts
196 → 196
Iterations
IterNodes
done5016
23164
11022
0354

prune1.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))) F))
0.2b
(/ (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))) F)
0.3b
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
15.4b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
486×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
159×unpow-prod-down
95×associate-/r*
58×add-exp-log
53×sqr-pow
41×div-exp
35×associate-/r/
33×associate-/l*
30×pow-unpow
25×div-inv
20×add-cbrt-cube
18×neg-sub0 pow-neg pow-sub
13×distribute-lft-neg-in distribute-rgt-neg-in
10×cbrt-undiv
6×pow-to-exp pow1 pow-exp
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×neg-mul-1 pow-pow pow-flip inv-pow associate-/l/
Counts
4 → 603
Calls
4 calls:
29.0ms
(/ 1 (/ (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))) F))
17.0ms
(/ (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))) F)
10.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
6.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

series1.5s

Counts
4 → 12
Calls
4 calls:
522.0ms
(/ 1 (/ (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))) F))
462.0ms
(/ (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))) F)
336.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
186.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify4.0s

Counts
615 → 615
Iterations
IterNodes
done5001
12555
0928

prune4.9s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes307.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.2b

bsearch366.0ms

Steps
ItersRangePoint
9
0.02586244036059231
12146952.384825662
8028.221689814058
10
-4.2073613499524506e+17
-55576812.421804816
-16640897351.893003

simplify11.0ms

Iterations
IterNodes
done47
147
040

end0.0ms

sample9.0s

Algorithm
intervals
Results
2.9s1643×body1280valid
2.4s1354×body640valid
1.8s4816×body80valid
958.0ms719×body320valid
338.0ms1579×body80nan
226.0ms346×body160valid