Details

Time bar (total: 18.4s)

sample136.0ms

Algorithm
intervals
Results
66.0ms131×body160valid
19.0ms125×body80valid

simplify955.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (230.0ms)

IterNodesCost
02664
18264
231355
3120954
done500054

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.2b
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.5b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
14.5b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

rewrite26.0ms

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 log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 78
Calls
4 calls:
10.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
11.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
1.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
1.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
51.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
293.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
624.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

simplify1.0s

Counts
90 → 90
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01382422
13012319
212142072
done50002038

prune701.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize71.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.2b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0))))
0.5b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
14.5b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
82×add-sqr-sqrt
73×times-frac
40×add-cube-cbrt *-un-lft-identity associate-*r*
32×sqrt-prod
27×add-exp-log
24×cbrt-prod
20×add-cbrt-cube
15×unswap-sqr
10×associate-*l*
8×cbrt-undiv div-exp prod-exp cbrt-unprod
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×fma-udef
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 140
Calls
4 calls:
5.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
73.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0))))
0.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
0.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

series1.3s

Counts
4 → 12
Calls
4 calls:
30.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
134.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0))))
394.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
709.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

simplify619.0ms

Counts
152 → 152
Iterations

Useful iterations: done (609.0ms)

IterNodesCost
02775192
17924933
done50004088

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0))))
0.2b
(* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))))
0.5b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592)
14.5b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
134×add-sqr-sqrt
106×times-frac
98×sqrt-prod
64×add-cube-cbrt *-un-lft-identity
56×associate-*r*
27×add-exp-log
26×associate-*l*
24×cbrt-prod unswap-sqr
21×pow1
20×add-cbrt-cube
18×swap-sqr
9×prod-exp cbrt-unprod
8×sqrt-pow1 pow1/2
7×cbrt-undiv div-exp
6×div-inv
5×pow-prod-up
4×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u add-log-exp
3×pow-sqr
2×frac-times associate-*r/ associate-*l/ *-commutative fma-udef
1×pow2 pow-plus sqrt-unprod rem-square-sqrt
Counts
4 → 200
Calls
4 calls:
66.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0))))
49.0ms
(* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))))
0.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592)
0.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

series2.0s

Counts
4 → 12
Calls
4 calls:
161.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0))))
95.0ms
(* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))))
625.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592)
1.1s
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fma (fabs x) 0.3275911 1.0))) (/ (cbrt 1.0) (sqrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429 -1.453152027) 1.421413741) (* (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (sqrt (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

simplify788.0ms

Counts
212 → 212
Iterations

Useful iterations: done (767.0ms)

IterNodesCost
03587243
19525931
done50015189

prune1.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (fma 0.3275911 (fabs x) 1.0))
0.5b
(fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592)
14.5b
(log (exp (fma (- (/ (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.0)))
14.5b
(fma (- (/ (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.0)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u log-prod log-pow log1p-expm1-u add-log-exp
3×exp-prod associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp rem-log-exp exp-sum clear-num div-inv
Counts
4 → 67
Calls
4 calls:
10.0ms
(/ 1.0 (fma 0.3275911 (fabs x) 1.0))
1.0ms
(fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592)
6.0ms
(log (exp (fma (- (/ (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.0)))
1.0ms
(fma (- (/ (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.0)

series1.6s

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 1.0 (fma 0.3275911 (fabs x) 1.0))
291.0ms
(fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592)
654.0ms
(log (exp (fma (- (/ (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.0)))
600.0ms
(fma (- (/ (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ (/ (pow (cbrt 1.0) 3) (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (fma (fabs x) 0.3275911 1.0))) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.0)

simplify1.1s

Counts
79 → 79
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01684130
13543852
213453049
done50013046

prune873.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 14.4b

regimes143.0ms

Accuracy

0% (0.0b remaining)

Error of 13.7b against oracle of 13.6b and baseline of 13.7b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02879
13179
done3179

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.8s3867×body160valid
474.0ms4133×body80valid