Details

Time bar (total: 29.7s)

sample226.0ms

Algorithm
intervals
Results
98.0ms56×body10240exit
46.0ms56×body1280valid
35.0ms335×body80valid
12.0ms25×body640valid
6.0ms19×body320valid
3.0ms13×body160valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5000
41391
3370
2124
147
019

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize58.0ms

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))))
3.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite257.0ms

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-cbrt-cube add-cube-cbrt
9×associate-*r*
8×add-exp-log
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 → 183
Calls
4 calls:
31.0ms
(* (- 1.0 eps) x)
67.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
93.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
56.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series485.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (- 1.0 eps) x)
61.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
78.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
291.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.2s

Counts
195 → 195
Iterations
IterNodes
done5000
24743
11327
0412

prune1.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (* (* x x) x) 0.6666666666666667 2.0)
0.1b
(* (* x x) x)
8.8b
(fma 1.0 (- (* x x)) (fma (* (* x x) x) 0.6666666666666667 2.0))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1
8×add-cbrt-cube add-exp-log
6×pow-plus pow-prod-up
5×add-sqr-sqrt
4×*-un-lft-identity add-cube-cbrt
3×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×pow2 pow-sqr fma-udef
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
3 → 50
Calls
3 calls:
1.0ms
(fma (* (* x x) x) 0.6666666666666667 2.0)
27.0ms
(* (* x x) x)
1.0ms
(fma 1.0 (- (* x x)) (fma (* (* x x) x) 0.6666666666666667 2.0))

series217.0ms

Counts
3 → 9
Calls
3 calls:
99.0ms
(fma (* (* x x) x) 0.6666666666666667 2.0)
42.0ms
(* (* x x) x)
76.0ms
(fma 1.0 (- (* x x)) (fma (* (* x x) x) 0.6666666666666667 2.0))

simplify1.9s

Counts
59 → 59
Iterations
IterNodes
done5001
31104
2421
1140
067

prune231.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (* x x) (- (* x 0.6666666666666667) 1.0))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube prod-diff add-exp-log
5×distribute-rgt-in add-sqr-sqrt distribute-lft-in
4×*-un-lft-identity add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×sub-neg associate-*r/
1×expm1-log1p-u flip3-- associate-*l* *-commutative log1p-expm1-u flip-- add-log-exp unswap-sqr
Counts
1 → 33
Calls
1 calls:
57.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

series119.0ms

Counts
1 → 3
Calls
1 calls:
119.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify3.2s

Counts
36 → 36
Iterations
IterNodes
done5007
33128
2770
1265
088

prune132.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- eps 1.0))
0.0b
(/ (exp (* x (- eps 1.0))) eps)
0.0b
(/ (exp (- (* x (+ 1.0 eps)))) eps)
3.2b
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ 1.0 eps)))) eps))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
209×*-un-lft-identity
171×add-sqr-sqrt
166×prod-diff
162×add-cube-cbrt
151×times-frac
120×exp-sum
71×distribute-rgt-in distribute-lft-in
32×distribute-neg-in
30×associate-/l*
21×distribute-lft-out
11×sub-neg
10×add-cbrt-cube
9×add-log-exp
8×add-exp-log
6×pow1 associate-/r* div-inv
5×associate-*r*
4×expm1-log1p-u fma-neg log1p-expm1-u
3×associate-*l* distribute-lft-out-- difference-of-squares
2×cbrt-undiv clear-num frac-2neg flip3-- diff-log div-exp associate-*r/ frac-sub flip-- associate-/l/
1×neg-sub0 exp-neg sum-log flip3-+ exp-diff pow-prod-down prod-exp associate--l+ *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 304
Calls
4 calls:
18.0ms
(* x (- eps 1.0))
39.0ms
(/ (exp (* x (- eps 1.0))) eps)
22.0ms
(/ (exp (- (* x (+ 1.0 eps)))) eps)
1.9s
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ 1.0 eps)))) eps))

series208.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* x (- eps 1.0))
40.0ms
(/ (exp (* x (- eps 1.0))) eps)
36.0ms
(/ (exp (- (* x (+ 1.0 eps)))) eps)
93.0ms
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ 1.0 eps)))) eps))

simplify2.9s

Counts
316 → 316
Iterations
IterNodes
done5002
23215
11201
0541

prune2.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes100.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 17.0b

bsearch313.0ms

Steps
ItersRangePoint
11
2.0412262699081644e-18
848.2985553752982
2.2270672321642286

simplify19.0ms

Iterations
IterNodes
done46
246
140
028

end0.0ms

sample8.3s

Algorithm
intervals
Results
2.3s1887×body10240exit
2.2s1792×body1280valid
1.7s10003×body80valid
1.2s1206×body640valid
253.0ms622×body320valid
168.0ms338×body160valid