Details

Time bar (total: 5.7s)

sample22.0ms

Algorithm
intervals
Results
5.0ms53×body640valid
3.0ms130×body80valid
3.0ms40×body320valid
2.0ms19×body1280valid
1.0ms14×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: 11.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (- x 1.0))
2.6b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
707×*-un-lft-identity
691×times-frac
514×add-sqr-sqrt
482×add-cube-cbrt
468×prod-diff
236×associate-+l+
91×distribute-lft-out
64×div-inv
56×associate-/r/
28×flip3-+ flip-+
18×fma-neg
17×distribute-lft-out--
12×difference-of-squares
10×fma-def add-log-exp
5×add-exp-log associate-/r* add-cbrt-cube
3×pow1 expm1-log1p-u flip3-- frac-add flip-- log1p-expm1-u associate-/l*
2×sub-neg diff-log sum-log frac-sub
1×cbrt-undiv +-commutative associate-+l- frac-2neg div-exp clear-num
Counts
3 → 583
Calls
3 calls:
73.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
10.0ms
(/ 1.0 (- x 1.0))
314.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series280.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
26.0ms
(/ 1.0 (- x 1.0))
215.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify145.0ms

Algorithm
egg-herbie
Counts
592 → 592
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0110810776
134078118
250017502

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
0.1b
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
10.7b
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
18.8b
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 2.0 x) 1)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity
27×times-frac
21×distribute-lft-out
19×add-sqr-sqrt add-cube-cbrt
16×unpow-prod-down cube-prod
11×add-log-exp
9×associate-/r*
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u associate-+r+ fma-def sum-cubes log1p-expm1-u
3×flip3-+ sum-log flip-+ fma-udef associate-/l*
2×+-commutative associate-/r/
1×cbrt-undiv associate-+r- sub-neg associate-+l+ frac-2neg diff-log div-exp prod-diff clear-num div-inv
Counts
4 → 103
Calls
4 calls:
17.0ms
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
38.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
6.0ms
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
0.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 2.0 x) 1)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
69.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
292.0ms
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
62.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (* (/ 2.0 x) 1)))

simplify62.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05091187
122561068
250021039

prune401.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
10.7b
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3)) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
10.7b
(cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3))
18.8b
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3)) (- (* (/ 2.0 x) 1)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
27×times-frac
22×add-sqr-sqrt add-cube-cbrt
21×distribute-lft-out
19×unpow-prod-down cube-prod
12×cbrt-prod
9×associate-/r*
6×add-exp-log add-cbrt-cube add-log-exp
4×pow1 expm1-log1p-u sum-cubes log1p-expm1-u
3×fma-def fma-udef associate-/l*
2×flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative cube-mult associate-+l+ associate-+r+ frac-2neg pow1/3 unpow3 div-exp clear-num sum-log rem-cbrt-cube div-inv sqr-pow
Counts
4 → 107
Calls
4 calls:
36.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
5.0ms
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3)) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
2.0ms
(cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3))
0.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3)) (- (* (/ 2.0 x) 1)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
294.0ms
(+ (fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3)) (- (* (/ 2.0 x) 1))) (fma (/ 2.0 x) (+ (- 1) 1) (/ 1.0 (- x 1.0))))
20.0ms
(cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3))
58.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (cbrt (pow (fma 1.0 (- 1.0 x) (pow x 2)) 3)) (- (* (/ 2.0 x) 1)))

simplify59.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04651216
120521118
250011091

prune444.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
61×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
27×add-exp-log
26×associate-/r*
15×div-exp
12×cube-prod sqr-pow
10×add-cbrt-cube
9×associate-/l*
7×pow-to-exp pow-exp
6×rec-exp 1-exp
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg clear-num div-inv
2×pow-flip inv-pow
1×fma-udef
Counts
4 → 187
Calls
4 calls:
0.0ms
(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
8.0ms
(/ 1 (pow x 5))
12.0ms
(/ 2.0 (pow x 3))
8.0ms
(/ 1 (pow x 7))

series269.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3)))
49.0ms
(/ 1 (pow x 5))
37.0ms
(/ 2.0 (pow x 3))
62.0ms
(/ 1 (pow x 7))

simplify48.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0450904
12278777
25001777

prune357.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch113.0ms

Steps
ItersRangePoint
10
26.826342714152005
1.350953981158519e+19
98.71861940061606
8
-4116.604674393256
-5.56536991933885
-98.62404855606621

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05329
16229
26229

end0.0ms

sample597.0ms

Algorithm
intervals
Results
188.0ms1887×body640valid
116.0ms4130×body80valid
76.0ms930×body320valid
70.0ms574×body1280valid
24.0ms480×body160valid