Details

Time bar (total: 6.2s)

sample99.0ms

Algorithm
intervals
Results
35.0ms240×body10240exit
31.0ms96×body1280valid
15.0ms87×body640valid
3.0ms33×body320valid
1.0ms20×body160valid
1.0ms20×body80valid

simplify47.0ms

Counts
1 → 1
Iterations

Useful iterations: 7 (46.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750017
done50017

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
1.3b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv expm1-udef
Counts
2 → 40
Calls
2 calls:
0.0ms
(fma 1 1 (exp (+ x x)))
5.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series93.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(fma 1 1 (exp (+ x x)))
71.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify76.0ms

Counts
46 → 46
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0150395
1512351
22464344
35002343
done5002343

prune117.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(- x (* 1/3 (pow x 3)))
0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b
(* 1/3 (pow x 3))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×associate-*r*
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log
5×add-cbrt-cube add-log-exp
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u fma-neg associate-*l* prod-diff prod-exp log1p-expm1-u
2×sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod fma-udef
Counts
3 → 63
Calls
3 calls:
5.0ms
(- x (* 1/3 (pow x 3)))
0.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
12.0ms
(* 1/3 (pow x 3))

series171.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(- x (* 1/3 (pow x 3)))
55.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
37.0ms
(* 1/3 (pow x 3))

simplify37.0ms

Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25001292
done5001292

prune166.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.6b
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.6b
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.6b
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×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
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
10.0ms
(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
1.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

series557.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
134.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
135.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
138.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))

simplify165.0ms

Counts
93 → 93
Iterations

Useful iterations: 3 (153.0ms)

IterNodesCost
03031267
110401174
246661078
350011030
done50011030

prune318.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.6b
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.7b
(pow (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) 6)
29.4b
(pow (pow (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) 6) 1/3)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
22×unpow-prod-down
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×cbrt-prod
7×add-exp-log
6×pow-unpow
5×pow1 pow-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow1/3 sqr-pow
1×unpow1/3
Counts
4 → 78
Calls
4 calls:
1.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
1.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
3.0ms
(pow (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) 6)
7.0ms
(pow (pow (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) 6) 1/3)

series724.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
139.0ms
(cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
190.0ms
(pow (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) 6)
260.0ms
(pow (pow (cbrt (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))) 6) 1/3)

simplify54.0ms

Counts
90 → 90
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04491064
11658991
25001908
done5001908

prune307.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 1.1b

regimes21.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0116
1136
2136
done136

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s7791×body10240exit
968.0ms3323×body1280valid
424.0ms2411×body640valid
131.0ms1237×body320valid
37.0ms574×body160valid
15.0ms455×body80valid