Details

Time bar (total: 7.2s)

sample23.0ms

Algorithm
intervals
Results
7.0ms65×body640valid
4.0ms134×body80valid
3.0ms32×body320valid
3.0ms18×body1280valid
0.0ms7×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (+ x 1.0))
2.0b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
725×*-un-lft-identity
703×times-frac
524×add-sqr-sqrt
492×add-cube-cbrt
468×prod-diff
236×associate-+l+
95×distribute-lft-out
65×div-inv
58×associate-/r/
29×flip3-+ flip-+
18×fma-neg
17×distribute-lft-out--
12×difference-of-squares
11×add-log-exp
10×fma-def
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num sum-log frac-sub
1×+-commutative associate-+l-
Counts
4 → 618
Calls
4 calls:
5.0ms
(/ 1.0 (- x 1.0))
52.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
5.0ms
(/ 1.0 (+ x 1.0))
236.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ 1.0 (- x 1.0))
44.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
29.0ms
(/ 1.0 (+ x 1.0))
229.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify156.0ms

Algorithm
egg-herbie
Counts
630 → 630
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
0115610955
136078288
250017670

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.2b
(pow (/ 1.0 (+ x 1.0)) 3)
2.0b
(+ (- (cbrt (pow (/ 1.0 (+ x 1.0)) 3)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
18.3b
(cbrt (pow (/ 1.0 (+ x 1.0)) 3))

rewrite720.0ms

Algorithm
rewrite-expression-head
Rules
792×*-un-lft-identity
788×times-frac
634×add-sqr-sqrt
600×cbrt-prod
597×add-cube-cbrt
587×associate-+l+
585×prod-diff
274×unpow-prod-down cube-prod
96×distribute-lft-out
76×div-inv
62×associate-/r/
32×flip3-+ flip-+
18×fma-def
17×sqr-pow
15×cube-mult unpow3
14×difference-of-squares
9×add-exp-log add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×cube-div pow-unpow frac-add associate-/l*
2×cbrt-undiv cbrt-div div-exp pow-exp sum-log distribute-lft-out-- rem-cube-cbrt
1×+-commutative pow-to-exp associate-+l- sub-neg flip3-- pow-pow frac-2neg pow1/3 diff-log clear-num frac-sub flip-- rem-cbrt-cube
Counts
4 → 772
Calls
4 calls:
5.0ms
(/ 1.0 (+ x 1.0))
8.0ms
(pow (/ 1.0 (+ x 1.0)) 3)
605.0ms
(+ (- (cbrt (pow (/ 1.0 (+ x 1.0)) 3)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
12.0ms
(cbrt (pow (/ 1.0 (+ x 1.0)) 3))

series349.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1.0 (+ x 1.0))
52.0ms
(pow (/ 1.0 (+ x 1.0)) 3)
238.0ms
(+ (- (cbrt (pow (/ 1.0 (+ x 1.0)) 3)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
27.0ms
(cbrt (pow (/ 1.0 (+ x 1.0)) 3))

simplify173.0ms

Algorithm
egg-herbie
Counts
784 → 784
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
087510701
140438211
250016984

prune1.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 2.0 (pow x 3))
0.0b
(- (- (* 2.0 (pow x 3))) (fma x 2.0 (/ 2.0 x)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
18×*-un-lft-identity prod-diff
16×add-cube-cbrt
12×associate-*r*
7×add-exp-log
6×fma-neg add-log-exp
4×distribute-lft-neg-in neg-mul-1 unpow-prod-down distribute-rgt-neg-in cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u diff-log log1p-expm1-u sqr-pow
1×associate--l- neg-sub0 cube-mult pow-to-exp sub-neg flip3-- unpow3 neg-log pow-exp *-commutative flip-- cbrt-unprod fma-udef associate--r+ distribute-lft-out-- difference-of-squares
Counts
2 → 76
Calls
2 calls:
7.0ms
(* 2.0 (pow x 3))
6.0ms
(- (- (* 2.0 (pow x 3))) (fma x 2.0 (/ 2.0 x)))

series100.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(* 2.0 (pow x 3))
57.0ms
(- (- (* 2.0 (pow x 3))) (fma x 2.0 (/ 2.0 x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0302779
11302526
25001507

prune137.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3)))))
0.1b
(/ 1 (pow x 5))
0.2b
(/ 1 (pow x 7))
0.3b
(/ 1 (pow x 3))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
61×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
31×add-exp-log
26×associate-/r*
18×div-exp
12×cube-prod sqr-pow
10×add-cbrt-cube
9×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
1×fma-udef
Counts
4 → 195
Calls
4 calls:
0.0ms
(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3)))))
4.0ms
(/ 1 (pow x 5))
4.0ms
(/ 1 (pow x 7))
5.0ms
(/ 1 (pow x 3))

series216.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (* 2.0 (/ 1 (pow x 3)))))
46.0ms
(/ 1 (pow x 5))
63.0ms
(/ 1 (pow x 7))
34.0ms
(/ 1 (pow x 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0440976
12301770
25002765

prune357.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.6b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04232
14232

end0.0ms

sample608.0ms

Algorithm
intervals
Results
204.0ms1894×body640valid
128.0ms4186×body80valid
76.0ms547×body1280valid
74.0ms903×body320valid
26.0ms470×body160valid