Details

Time bar (total: 31.2s)

sample295.0ms

Algorithm
intervals
Results
114.0ms67×body10240exit
49.0ms344×body80valid
40.0ms34×body1280valid
29.0ms47×body640valid
12.0ms28×body320valid
3.0ms11×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
01929
14629
212229
337727
4226727
done500027

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.5b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
81×exp-neg frac-sub
80×frac-times
61×neg-sub0 exp-diff
40×associate-*r/ associate-*l/
31×flip3-- flip--
30×flip3-+ flip-+
20×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
6×add-exp-log exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log difference-of-squares unswap-sqr
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac diff-log neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 168
Calls
4 calls:
22.0ms
(exp (- (* (- 1.0 eps) x)))
100.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
131.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
100.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series650.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(exp (- (* (- 1.0 eps) x)))
94.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
104.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
400.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.0s

Counts
180 → 180
Iterations

Useful iterations: done (999.0ms)

IterNodesCost
03788233
112157479
done50007161

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
5.8b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
33.0ms
(* 0.6666666666666667 (pow x 3))
126.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series140.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(* 0.6666666666666667 (pow x 3))
78.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify879.0ms

Counts
51 → 51
Iterations

Useful iterations: done (877.0ms)

IterNodesCost
084590
1222548
2908500
done5000462

prune309.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
16×exp-sum
15×times-frac
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×distribute-rgt-in distribute-lft-in
10×add-log-exp
8×distribute-neg-in
6×sub-neg associate-+r+ add-cbrt-cube
5×add-exp-log associate-/l*
4×pow1 associate-*r/ frac-add
3×associate-/r*
2×exp-prod exp-to-pow flip3-+ associate--l+ frac-sub flip-+ rem-exp-log associate-/l/
1×cbrt-undiv +-commutative neg-sub0 exp-neg flip3-- frac-2neg exp-diff div-exp clear-num sum-log flip-- div-inv
Counts
4 → 86
Calls
4 calls:
15.0ms
(exp (* x (- eps 1.0)))
15.0ms
(exp (* x (- eps 1.0)))
27.0ms
(/ (exp (- (* x (+ eps 1.0)))) eps)
196.0ms
(+ (/ (* (exp (* x (- eps 1.0))) 1.0) eps) (* 1.0 (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(exp (* x (- eps 1.0)))
32.0ms
(exp (* x (- eps 1.0)))
60.0ms
(/ (exp (- (* x (+ eps 1.0)))) eps)
326.0ms
(+ (/ (* (exp (* x (- eps 1.0))) 1.0) eps) (* 1.0 (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps))))

simplify2.1s

Counts
98 → 98
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02232386
15662220
225392062
done50012048

prune881.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize125.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (* 1.0 (+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))))
4.1b
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))
4.1b
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))
4.1b
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))

rewrite3.9s

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity add-log-exp
16×frac-add
12×sum-log distribute-lft-out
9×associate-+l+
8×flip3-+ frac-sub flip-+
6×cbrt-div diff-log associate-*r/ distribute-lft-out--
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt flip3-- add-cbrt-cube flip--
3×+-commutative associate-+l- sub-neg associate--l+
1×cbrt-prod pow1/3
Counts
4 → 87
Calls
4 calls:
588.0ms
(cbrt (* 1.0 (+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))))
1.1s
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))
1.1s
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))
1.2s
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
485.0ms
(cbrt (* 1.0 (+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))))
202.0ms
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))
216.0ms
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))
217.0ms
(+ (- (+ (exp (- (* x (+ eps 1.0)))) (exp (* x (- eps 1.0)))) (/ (exp (- (* x (+ eps 1.0)))) eps)) (/ (exp (* (- eps 1.0) x)) eps))

simplify2.5s

Counts
99 → 99
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02356341
16855756
233105421
done50025374

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes192.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.7b

bsearch397.0ms

Steps
ItersRangePoint
10
6.6778646084690235e-09
20905.191039111578
332.9441210839744

simplify22.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
036131
149131
257131
359131
done59131

end0.0ms

sample11.0s

Algorithm
intervals
Results
3.4s1922×body10240exit
2.7s9927×body80valid
2.0s1680×body1280valid
1.1s1314×body640valid
878.0ms654×body320valid
90.0ms321×body160valid