Details

Time bar (total: 8.3s)

sample34.0ms

Algorithm
intervals
Results
14.0ms79×body1280valid
6.0ms57×body640valid
3.0ms181×body80valid
1.0ms20×body320valid
1.0ms14×body160valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0103
1133
2153
3153
done153

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
4.1b
(- (exp x) 1.0)

rewrite42.0ms

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-exp-log add-cbrt-cube add-log-exp
3×fma-neg associate-/r*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 68
Calls
2 calls:
25.0ms
(/ (- (exp x) 1.0) x)
15.0ms
(- (exp x) 1.0)

series58.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(/ (- (exp x) 1.0) x)
15.0ms
(- (exp x) 1.0)

simplify35.0ms

Counts
74 → 74
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0282468
1919380
25001377
done5001377

prune139.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b
(fma 1/6 (pow x 2) (fma 1/2 x 1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma 1/6 (pow x 2) (fma 1/2 x 1))

series21.0ms

Counts
1 → 3
Calls
1 calls:
21.0ms
(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify25.0ms

Counts
13 → 13
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03659
110452
253552
3500252
done500252

prune35.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
0.0b
(pow (exp x) 3)
0.0b
(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
4.1b
(- (pow (exp x) 3) (pow 1.0 3))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
717×add-sqr-sqrt
612×times-frac
479×*-un-lft-identity
309×add-cube-cbrt
282×unpow-prod-down cube-prod
272×difference-of-squares
162×sqr-pow
144×prod-diff
104×associate-/l*
85×distribute-lft-out--
26×cube-mult unpow3
17×difference-cubes
12×fma-neg add-cbrt-cube
11×add-exp-log
6×associate-/r* div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u pow-pow div-exp log1p-expm1-u
3×pow-unpow exp-prod div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×pow-to-exp sub-neg diff-log pow-exp rem-cube-cbrt
Counts
4 → 677
Calls
4 calls:
84.0ms
(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
4.0ms
(pow (exp x) 3)
91.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
37.0ms
(- (pow (exp x) 3) (pow 1.0 3))

series300.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
23.0ms
(pow (exp x) 3)
94.0ms
(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
46.0ms
(- (pow (exp x) 3) (pow 1.0 3))

simplify136.0ms

Counts
689 → 689
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0157012187
1500211358
done500211358

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (exp x) 3) 3)
0.0b
(/ (/ (- (pow (pow (exp x) 3) 3) (pow (pow 1.0 3) 3)) (fma (pow 1.0 3) (+ (pow (exp x) 3) (pow 1.0 3)) (pow (exp x) 6))) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
0.0b
(pow (exp x) 6)
4.0b
(- (pow (pow (exp x) 3) 3) (pow (pow 1.0 3) 3))

rewrite771.0ms

Algorithm
rewrite-expression-head
Rules
3157×add-sqr-sqrt
3147×unpow-prod-down
3144×cube-prod
2637×times-frac
1883×*-un-lft-identity
1337×add-cube-cbrt
1300×difference-of-squares
967×sqr-pow
900×prod-diff
379×associate-/l*
273×distribute-lft-out--
186×cube-mult unpow3
30×fma-neg
13×difference-cubes
10×add-exp-log add-cbrt-cube
6×pow-unpow add-log-exp
5×pow1 pow-pow pow-exp div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv pow-to-exp exp-prod div-exp associate-/r*
2×div-sub
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- associate-/l/ rem-cube-cbrt
Counts
4 → 2670
Calls
4 calls:
7.0ms
(pow (pow (exp x) 3) 3)
310.0ms
(/ (/ (- (pow (pow (exp x) 3) 3) (pow (pow 1.0 3) 3)) (fma (pow 1.0 3) (+ (pow (exp x) 3) (pow 1.0 3)) (pow (exp x) 6))) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
4.0ms
(pow (exp x) 6)
132.0ms
(- (pow (pow (exp x) 3) 3) (pow (pow 1.0 3) 3))

series406.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(pow (pow (exp x) 3) 3)
261.0ms
(/ (/ (- (pow (pow (exp x) 3) 3) (pow (pow 1.0 3) 3)) (fma (pow 1.0 3) (+ (pow (exp x) 3) (pow 1.0 3)) (pow (exp x) 6))) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
37.0ms
(pow (exp x) 6)
60.0ms
(- (pow (pow (exp x) 3) 3) (pow (pow 1.0 3) 3))

simplify750.0ms

Counts
2682 → 2682
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0314881392
1500275068
done500275068

prune3.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.2b

bsearch35.0ms

Steps
ItersRangePoint
10
-0.001391736753177052
-4.1211929036737376e-16
-0.00016604344095812133

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02816
12816
done2816

end0.0ms

sample883.0ms

Algorithm
intervals
Results
367.0ms2262×body1280valid
167.0ms1661×body640valid
99.0ms5474×body80valid
57.0ms888×body320valid
16.0ms395×body160valid