Details

Time bar (total: 5.4s)

sample113.0ms

Algorithm
intervals
Results
31.0ms69×body1280valid
31.0ms66×body10240exit
18.0ms323×body80valid
10.0ms38×body640valid
4.0ms23×body320valid
1.0ms7×body160valid

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (35.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 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))))
1.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 173
Calls
4 calls:
7.0ms
(* (- 1.0 eps) x)
12.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
15.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
17.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (- 1.0 eps) x)
47.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
54.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
197.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify147.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
012534065
147123787
250013778

prune462.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.6666666666666667 (pow x 3))
4.6b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

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:
6.0ms
(* 0.6666666666666667 (pow x 3))
7.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series82.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(* 0.6666666666666667 (pow x 3))
40.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune111.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x eps) (* 1.0 x))
0.0b
(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
0.0b
(/ (exp (- (* x eps) (* 1.0 x))) eps)
1.2b
(+ (* 1.0 (- (+ (exp (- (+ (* x eps) (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x)))) (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))) (* 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
27×times-frac
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×associate-*r/ exp-sum
9×associate-/l*
8×frac-add add-cbrt-cube add-log-exp
6×add-exp-log sub-neg associate-+l+ associate-/r*
5×exp-diff
4×pow1 distribute-neg-in frac-sub
3×distribute-rgt-in distribute-lft-in flip3-+ flip-+ associate-/l/
2×cbrt-undiv +-commutative neg-sub0 exp-neg frac-2neg div-exp associate--l+ clear-num sum-log div-inv
1×flip3-- flip-- distribute-lft-out
Counts
4 → 104
Calls
4 calls:
4.0ms
(+ (* x eps) (* 1.0 x))
10.0ms
(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
7.0ms
(/ (exp (- (* x eps) (* 1.0 x))) eps)
23.0ms
(+ (* 1.0 (- (+ (exp (- (+ (* x eps) (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x)))) (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))) (* 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (* x eps) (* 1.0 x))
30.0ms
(/ (exp (- (+ (* x eps) (* 1.0 x)))) eps)
31.0ms
(/ (exp (- (* x eps) (* 1.0 x))) eps)
178.0ms
(+ (* 1.0 (- (+ (exp (- (+ (* x eps) (* 1.0 x)))) (exp (- (* x eps) (* 1.0 x)))) (/ (exp (- (+ (* x eps) (* 1.0 x)))) eps))) (* 1.0 (/ (exp (- (* x eps) (* 1.0 x))) eps)))

simplify75.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06501859
124081769
250011758

prune392.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes51.0ms

Accuracy

95.8% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.9b

bsearch155.0ms

Steps
ItersRangePoint
10
3.9524390088012255e-07
7103758.057079569
130.4040333957902

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04533
15733
25733

end0.0ms

sample2.9s

Algorithm
intervals
Results
793.0ms1902×body10240exit
765.0ms1689×body1280valid
586.0ms10213×body80valid
331.0ms1265×body640valid
111.0ms617×body320valid
37.0ms326×body160valid