Details

Time bar (total: 42.8s)

sample737.0ms

Algorithm
intervals
Results
270.0ms54×body1280valid
101.0ms38×body640valid
98.0ms157×body80valid
53.0ms54×body80nan
16.0ms14×body320valid
12.0ms16×body160valid

simplify3.2s

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

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.4b

localize60.0ms

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))))
16.2b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite85.0ms

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:
13.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
23.0ms
(* (/ 1.0 (tan B)) x)
17.0ms
(/ (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)))

series1.2s

Counts
4 → 12
Calls
4 calls:
446.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
140.0ms
(* (/ 1.0 (tan B)) x)
341.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
237.0ms
(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

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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))))
16.2b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
213×times-frac
128×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
51×unpow-prod-down
37×associate-/r*
30×pow-unpow
22×add-exp-log
17×sqr-pow
13×distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
12×associate-/r/
11×div-exp
9×div-inv associate-/l*
6×neg-sub0 pow-neg pow-sub
5×pow1 cbrt-undiv
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 tan-quot
Counts
4 → 257
Calls
4 calls:
11.0ms
(/ x (tan B))
24.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
18.0ms
(/ (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:
147.0ms
(/ x (tan B))
464.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
338.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
229.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.7s

Counts
269 → 269
Iterations
IterNodes
done5004
24052
11238
0480

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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))))
16.2b
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
86×times-frac
61×*-un-lft-identity
57×add-cube-cbrt
56×add-exp-log
27×unpow-prod-down
25×associate-*r*
24×div-exp
20×add-cbrt-cube
16×prod-exp
13×pow-unpow associate-*l*
12×unswap-sqr
11×sqr-pow
10×associate-/r*
7×pow1
6×pow-to-exp cbrt-undiv pow-exp associate-/l*
5×div-inv
4×expm1-log1p-u rec-exp 1-exp cbrt-unprod log1p-expm1-u 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 → 190
Calls
4 calls:
6.0ms
(/ x (tan B))
12.0ms
(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
32.0ms
(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
4.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
163.0ms
(/ x (tan B))
782.0ms
(/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0)))
497.0ms
(* (/ 1 (sin B)) (/ F (pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))))
167.0ms
(pow (fma F F (fma x 2.0 2.0)) (/ 1.0 2.0))

simplify2.8s

Counts
202 → 202
Iterations
IterNodes
done5013
22900
1962
0353

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ x (sin B)) (cos 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))))
16.2b
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

rewrite102.0ms

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
13×distribute-lft-neg-in distribute-rgt-neg-in associate-*l*
11×div-exp associate-/r/
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/ *-commutative
Counts
4 → 261
Calls
4 calls:
46.0ms
(* (/ x (sin B)) (cos B))
20.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
9.0ms
(/ (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)))

series1.1s

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (/ x (sin B)) (cos B))
421.0ms
(/ F (/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))))
288.0ms
(/ (sin B) (pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0))))
255.0ms
(pow (fma F F (fma x 2.0 2.0)) (- (/ 1.0 2.0)))

simplify3.8s

Counts
273 → 273
Iterations
IterNodes
done5002
24344
11296
0488

prune2.2s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes510.0ms

Accuracy

97.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.3b

bsearch449.0ms

Steps
ItersRangePoint
10
1.415873715001122e+23
1.34232255763024e+37
1.0855066767324344e+24
7
-84463.33967257517
-1026.6337297585196
-73198.40425548062

simplify16.0ms

Iterations
IterNodes
done46
146
041

end0.0ms

sample9.0s

Algorithm
intervals
Results
3.0s1709×body1280valid
1.7s1420×body640valid
1.3s4667×body80valid
1.1s354×body160valid
997.0ms710×body320valid
321.0ms1640×body80nan