Details

Time bar (total: 27.6s)

sample45.0ms

Algorithm
intervals
Results
17.0ms86×body1280valid
7.0ms54×body640valid
4.0ms154×body80valid
3.0ms35×body320valid
1.0ms15×body160valid

simplify32.0ms

Counts
1 → 1
Iterations
IterNodes
done15
315
213
110
05

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
4.6b
(- (exp x) 1.0)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* fma-neg
2×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 70
Calls
2 calls:
51.0ms
(/ (- (exp x) 1.0) x)
17.0ms
(- (exp x) 1.0)

series101.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ (- (exp x) 1.0) x)
33.0ms
(- (exp x) 1.0)

simplify4.4s

Counts
76 → 76
Iterations
IterNodes
done5001
32314
2719
1294
0129

prune564.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x (fma x 1/6 1/2) 1)
0.1b
(fma x 1/6 1/2)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
2 → 22
Calls
2 calls:
1.0ms
(fma x (fma x 1/6 1/2) 1)
1.0ms
(fma x 1/6 1/2)

series103.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(fma x (fma x 1/6 1/2) 1)
65.0ms
(fma x 1/6 1/2)

simplify5.4s

Counts
28 → 28
Iterations
IterNodes
done5001
42323
3430
2116
157
036

prune338.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize114.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))
0.0b
(/ (/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))) x)
0.0b
(/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x)))))
4.6b
(- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
56×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv add-log-exp
4×expm1-log1p-u pow1 cbrt-undiv fma-neg div-exp prod-diff insert-posit16 log1p-expm1-u
3×div-sub fma-udef associate-/l/
2×clear-num frac-2neg flip3-- exp-sum flip--
1×sub-neg diff-log
Counts
4 → 141
Calls
4 calls:
2.0ms
(fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))
73.0ms
(/ (/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))) x)
73.0ms
(/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x)))))
34.0ms
(- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0))

series723.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))
326.0ms
(/ (/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))) x)
244.0ms
(/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x)))))
55.0ms
(- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0))

simplify3.7s

Counts
153 → 153
Iterations
IterNodes
done5002
21670
1587
0247

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize127.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))
0.0b
(/ (* (/ 1 (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x)))))) (/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))) x)
0.7b
(/ 1 (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))
4.6b
(- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
42×add-exp-log
39×times-frac
38×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
26×add-cbrt-cube
24×sqrt-prod
20×div-exp
15×associate-/r*
11×cbrt-undiv
8×prod-exp
7×associate-/l*
6×pow1 add-log-exp
5×associate-/l/
4×expm1-log1p-u fma-neg prod-diff cbrt-unprod insert-posit16 log1p-expm1-u
3×rec-exp clear-num frac-2neg 1-exp div-inv pow-flip
2×flip3-- exp-sum fma-udef flip--
1×frac-times sub-neg sqrt-pow1 pow1/2 diff-log div-sub associate-*l/ associate-*r/ inv-pow
Counts
4 → 153
Calls
4 calls:
73.0ms
(/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))
43.0ms
(/ (* (/ 1 (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x)))))) (/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))) x)
9.0ms
(/ 1 (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))
31.0ms
(- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
510.0ms
(/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))
307.0ms
(/ (* (/ 1 (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x)))))) (/ (- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0)) (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))) x)
242.0ms
(/ 1 (sqrt (fma (exp x) (exp x) (* 1.0 (+ 1.0 (exp x))))))
58.0ms
(- (exp (fma x 2 x)) (* (* 1.0 1.0) 1.0))

simplify4.7s

Counts
165 → 165
Iterations
IterNodes
done5005
22277
1680
0282

prune1.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes87.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch52.0ms

Steps
ItersRangePoint
10
-3720466.2051109266
-6.803810524357175e-07
-0.00010786855983473736

simplify19.0ms

Iterations
IterNodes
done31
131
025

end0.0ms

sample2.1s

Algorithm
intervals
Results
700.0ms2283×body1280valid
677.0ms1645×body640valid
256.0ms5518×body80valid
129.0ms831×body320valid
32.0ms411×body160valid