Details

Time bar (total: 26.7s)

sample246.0ms

Algorithm
intervals
Results
79.0ms314×body80valid
61.0ms73×body10240exit
47.0ms60×body1280valid
18.0ms45×body640valid
6.0ms20×body320valid
2.0ms12×body160valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done5001
42356
3395
2124
147
019

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (+ 1.0 eps))
0.0b
(* x (- eps 1.0))
0.0b
(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps))))
4.4b
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
49×*-un-lft-identity
36×times-frac
33×add-cube-cbrt
19×distribute-rgt-in distribute-lft-in
18×prod-diff
14×exp-sum
13×difference-of-squares
10×add-cbrt-cube
9×associate-*r* add-exp-log
8×pow1
7×distribute-lft-out--
6×associate-*l* associate-/l*
5×associate-/r*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
2×sub-neg flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ div-sub div-exp flip-+ fma-udef div-inv distribute-lft-out
Counts
4 → 139
Calls
4 calls:
31.0ms
(* x (+ 1.0 eps))
36.0ms
(* x (- eps 1.0))
46.0ms
(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps))))
0.0ms
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* x (+ 1.0 eps))
49.0ms
(* x (- eps 1.0))
49.0ms
(/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps))))
149.0ms
(fma (exp (* x (- eps 1.0))) (+ (/ 1.0 eps) 1.0) (/ (- 1.0 (/ 1.0 eps)) (exp (* x (+ 1.0 eps)))))

simplify3.0s

Counts
151 → 151
Iterations
IterNodes
done5001
23045
1749
0292

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (* x x))
0.2b
(/ 2.7755575615628914e-17 (/ eps (* x (* x x))))
2.8b
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (* x (* x x)))))
2.9b
(/ eps (* x (* x x)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
32×add-cbrt-cube add-exp-log
24×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
18×pow1
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
8×associate-/r*
6×div-inv associate-/l*
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* pow-prod-down
2×clear-num frac-2neg
1×pow2 pow-plus cube-unmult associate-*r* associate-/r/ pow-sqr *-commutative fma-udef unswap-sqr
Counts
4 → 113
Calls
4 calls:
14.0ms
(* x (* x x))
19.0ms
(/ 2.7755575615628914e-17 (/ eps (* x (* x x))))
0.0ms
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (* x (* x x)))))
18.0ms
(/ eps (* x (* x x)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* x (* x x))
71.0ms
(/ 2.7755575615628914e-17 (/ eps (* x (* x x))))
62.0ms
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (* x (* x x)))))
45.0ms
(/ eps (* x (* x x)))

simplify2.9s

Counts
125 → 125
Iterations
IterNodes
done5000
23286
1448
0168

prune688.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ eps (log (exp (* x (* x x)))))
0.1b
(* x (* x x))
1.3b
(log (exp (* x (* x x))))
2.8b
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (log (exp (* x (* x x)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
18×add-sqr-sqrt times-frac
17×*-un-lft-identity add-cube-cbrt
15×log-pow
11×add-cbrt-cube add-exp-log
9×add-log-exp
6×associate-/r*
5×exp-prod exp-to-pow pow-prod-up
4×expm1-log1p-u log1p-expm1-u
3×log-prod associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l*
1×pow2 cbrt-undiv clear-num frac-2neg pow-plus cube-unmult div-exp rem-log-exp associate-*r* pow-sqr *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 93
Calls
4 calls:
5.0ms
(/ eps (log (exp (* x (* x x)))))
15.0ms
(* x (* x x))
4.0ms
(log (exp (* x (* x x))))
0.0ms
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (log (exp (* x (* x x)))))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ eps (log (exp (* x (* x x)))))
43.0ms
(* x (* x x))
45.0ms
(log (exp (* x (* x x))))
64.0ms
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (log (exp (* x (* x x)))))))

simplify1.7s

Counts
105 → 105
Iterations
IterNodes
done5000
21737
1276
0126

prune605.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (* x x))
1.3b
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
1.3b
(log (cbrt (exp (* x (* x x)))))
2.8b
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (+ (log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x)))))) (log (cbrt (exp (* x (* x x)))))))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
27×pow1
13×add-exp-log
11×log-pow
9×add-cbrt-cube
8×add-sqr-sqrt
7×log-prod *-un-lft-identity pow1/3 pow-prod-up add-cube-cbrt
5×pow-prod-down
4×expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×cbrt-prod rem-log-exp associate-*l* pow-sqr cbrt-unprod
2×pow2 pow-plus
1×cube-unmult associate-*r* *-commutative fma-udef unswap-sqr
Counts
4 → 75
Calls
4 calls:
17.0ms
(* x (* x x))
15.0ms
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
8.0ms
(log (cbrt (exp (* x (* x x)))))
1.0ms
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (+ (log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x)))))) (log (cbrt (exp (* x (* x x)))))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
44.0ms
(* x (* x x))
944.0ms
(log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x))))))
973.0ms
(log (cbrt (exp (* x (* x x)))))
499.0ms
(fma (* x x) 1.0 (/ 2.7755575615628914e-17 (/ eps (+ (log (* (cbrt (exp (* x (* x x)))) (cbrt (exp (* x (* x x)))))) (log (cbrt (exp (* x (* x x)))))))))

simplify1.2s

Counts
87 → 87
Iterations
IterNodes
done5001
21158
1215
0106

prune642.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

regimes167.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.0b

bsearch254.0ms

Steps
ItersRangePoint
9
6.220956769517991e-07
20.852008069825544
1.4216286406050425

simplify10.0ms

Iterations
IterNodes
done32
132
026

end0.0ms

sample9.0s

Algorithm
intervals
Results
2.3s1723×body1280valid
2.2s2000×body10240exit
2.1s1285×body640valid
1.4s10052×body80valid
287.0ms669×body320valid
84.0ms347×body160valid