Details

Time bar (total: 7.7s)

sample45.0ms

Algorithm
intervals
Results
15.0ms124×body160valid
8.0ms132×body80valid

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (26.0ms)

IterNodesCost
08236
131036
2105431
3485530
4500130
done500130

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.5b
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
13.8b
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ fma-udef div-inv
Counts
4 → 82
Calls
4 calls:
9.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
10.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
0.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

series650.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
33.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
217.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)
370.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

simplify42.0ms

Counts
94 → 94
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
03351396
113571221
250011163
done50011163

prune508.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(/ (- 1.0) (fma (fabs x) 0.3275911 1.0))
0.5b
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
13.8b
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
39×times-frac
35×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-/l*
12×distribute-lft-neg-in distribute-rgt-neg-in
8×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1 expm1-log1p-u neg-mul-1 log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num associate-/r/ fma-udef div-inv
1×neg-sub0 flip3-+ div-sub distribute-frac-neg flip-+
Counts
4 → 110
Calls
4 calls:
9.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
8.0ms
(/ (- 1.0) (fma (fabs x) 0.3275911 1.0))
0.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
0.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

series846.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
36.0ms
(/ (- 1.0) (fma (fabs x) 0.3275911 1.0))
276.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
504.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)

simplify50.0ms

Counts
122 → 122
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04851574
118411414
250021386
done50021386

prune659.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 1.0) (fma (fabs x) 0.3275911 1.0))
0.5b
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
13.8b
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)
13.8b
(log (exp (fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
29×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u neg-mul-1 log-prod log-pow log1p-expm1-u add-log-exp
3×exp-prod associate-/r* fma-udef
1×cbrt-undiv neg-sub0 frac-2neg div-sub distribute-frac-neg div-exp rem-log-exp exp-sum clear-num div-inv
Counts
4 → 97
Calls
4 calls:
8.0ms
(/ (- 1.0) (fma (fabs x) 0.3275911 1.0))
0.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
0.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)
3.0ms
(log (exp (fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (- 1.0) (fma (fabs x) 0.3275911 1.0))
273.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
491.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)
492.0ms
(log (exp (fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)))

simplify49.0ms

Counts
109 → 109
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
04102274
114542013
250011932
done50011932

prune636.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (fma (fabs x) 0.3275911 1.0))
0.3b
(* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))
0.5b
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
13.8b
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (* (/ (* (cbrt (- 1.0)) (cbrt (- 1.0))) (* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) (/ (cbrt (- 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) 1.0)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×cbrt-prod
13×add-cube-cbrt *-un-lft-identity
11×pow1
7×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up fma-udef
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 75
Calls
4 calls:
1.0ms
(cbrt (fma (fabs x) 0.3275911 1.0))
11.0ms
(* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))
0.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
0.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (* (/ (* (cbrt (- 1.0)) (cbrt (- 1.0))) (* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) (/ (cbrt (- 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (fma (fabs x) 0.3275911 1.0))
146.0ms
(* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))
273.0ms
(fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736)
569.0ms
(fma (/ (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (expm1 (log1p (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x)))) (* (/ (* (cbrt (- 1.0)) (cbrt (- 1.0))) (* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) (/ (cbrt (- 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) 1.0)

simplify46.0ms

Counts
87 → 87
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02981528
112311306
250011213
done50011213

prune469.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.7b

regimes142.0ms

Accuracy

0% (0.0b remaining)

Error of 13.6b against oracle of 13.5b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03134
13134
done3134

end0.0ms

sample883.0ms

Algorithm
intervals
Results
479.0ms3838×body160valid
261.0ms4162×body80valid