Details

Time bar (total: 20.8s)

sample241.0ms

Algorithm
intervals
Results
79.0ms63×body10240exit
52.0ms55×body1280valid
44.0ms343×body80valid
20.0ms32×body640valid
10.0ms26×body320valid
4.0ms14×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (377.0ms)

IterNodesCost
01929
14729
212429
339527
4233826
done500226

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.9b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 eps) x)
2.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
42×associate-*l/
38×associate-*r/
32×flip3-- flip--
28×flip3-+ flip-+
23×add-sqr-sqrt
19×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×add-exp-log associate-*r*
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out
Counts
4 → 176
Calls
4 calls:
35.0ms
(* (- 1.0 eps) x)
74.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms
(* (+ 1.0 eps) x)
77.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series454.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (- 1.0 eps) x)
90.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
34.0ms
(* (+ 1.0 eps) x)
287.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify827.0ms

Counts
188 → 188
Iterations

Useful iterations: done (814.0ms)

IterNodesCost
04068061
113997235
done50007031

prune772.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
7.2b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×fma-neg prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 31
Calls
2 calls:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
10.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

series194.0ms

Counts
2 → 6
Calls
2 calls:
128.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
66.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (pow x 2)))

simplify657.0ms

Counts
37 → 37
Iterations

Useful iterations: done (655.0ms)

IterNodesCost
053544
1138530
2634468
done5000433

prune180.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3)
0.0b
(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
3.8b
(cbrt (pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
12×cbrt-prod
10×unpow-prod-down
9×add-exp-log
8×associate-*l*
6×cube-prod prod-diff add-cbrt-cube
5×distribute-rgt-in distribute-lft-in
4×pow1 cube-div unswap-sqr sqr-pow
3×expm1-log1p-u pow-unpow associate-*r* prod-exp log1p-expm1-u add-log-exp
2×cube-mult pow-to-exp sub-neg cbrt-div flip3-+ unpow3 associate-*r/ pow-exp flip-+ unpow2
1×flip3-- pow-pow pow1/3 *-commutative flip-- rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
3 → 93
Calls
3 calls:
16.0ms
(pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3)
68.0ms
(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
7.0ms
(cbrt (pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3))

series310.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3)
136.0ms
(* (pow x 2) (- (* 0.6666666666666667 x) 1.0))
53.0ms
(cbrt (pow (+ 2.0 (* (pow x 2) (- (* 0.6666666666666667 x) 1.0))) 3))

simplify2.5s

Counts
102 → 102
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01861981
15101699
227581432
done50011429

prune338.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (- (exp (- (* (+ 1.0 eps) x)))) (- (/ 1.0 eps) 1.0))
0.0b
(* (+ 1.0 eps) x)
4.1b
(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (* (- (exp (- (* (+ 1.0 eps) x)))) (- (/ 1.0 eps) 1.0)))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
93×add-sqr-sqrt
86×*-un-lft-identity
80×add-cube-cbrt
78×prod-diff
55×times-frac
41×distribute-rgt-in distribute-lft-in
19×associate-*l*
12×associate-*r*
10×pow1 add-exp-log add-cbrt-cube
6×associate-*l/ div-inv distribute-neg-frac
4×expm1-log1p-u frac-times flip3-- flip-- log1p-expm1-u add-log-exp
3×neg-sub0 distribute-lft-neg-in exp-neg distribute-rgt-neg-in exp-diff pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×sub-neg associate-*r/ distribute-lft-out--
1×distribute-lft-neg-out neg-mul-1 flip3-+ flip-+ fma-udef distribute-lft-out
Counts
4 → 178
Calls
4 calls:
27.0ms
(* (- 1.0 eps) x)
116.0ms
(* (- (exp (- (* (+ 1.0 eps) x)))) (- (/ 1.0 eps) 1.0))
23.0ms
(* (+ 1.0 eps) x)
1.0ms
(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (* (- (exp (- (* (+ 1.0 eps) x)))) (- (/ 1.0 eps) 1.0)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (- 1.0 eps) x)
70.0ms
(* (- (exp (- (* (+ 1.0 eps) x)))) (- (/ 1.0 eps) 1.0))
37.0ms
(* (+ 1.0 eps) x)
291.0ms
(fma (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))) (* (- (exp (- (* (+ 1.0 eps) x)))) (- (/ 1.0 eps) 1.0)))

simplify779.0ms

Counts
190 → 190
Iterations

Useful iterations: done (762.0ms)

IterNodesCost
03515362
19994751
done50004048

prune622.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes104.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.5b

bsearch310.0ms

Steps
ItersRangePoint
10
1.5458422377508842e-07
302474.8861676866
378.4237213355006

simplify15.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03349
15049
26249
36349
done6349

end0.0ms

sample9.7s

Algorithm
intervals
Results
4.2s2005×body10240exit
1.8s1710×body1280valid
1.7s10000×body80valid
1.0s1296×body640valid
311.0ms642×body320valid
75.0ms320×body160valid