Details

Time bar (total: 6.0s)

sample23.0ms

Algorithm
intervals
Results
6.0ms61×body640valid
4.0ms129×body80valid
3.0ms21×body1280valid
3.0ms33×body320valid
1.0ms12×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 10.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.3b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite361.0ms

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:
8.0ms
(/ 1.0 (+ x 1.0))
5.0ms
(/ 1.0 (- x 1.0))
51.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
245.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(/ 1.0 (+ x 1.0))
28.0ms
(/ 1.0 (- x 1.0))
48.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
239.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify159.0ms

Algorithm
egg-herbie
Counts
630 → 630
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
0115610955
136078288
250017670

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
0.6b
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
0.6b
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
29.8b
(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
40×*-un-lft-identity
30×cbrt-prod
24×times-frac
12×difference-of-squares
9×cbrt-div distribute-lft-out--
7×add-cube-cbrt
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 frac-sub flip-- distribute-lft-out
1×fma-udef
Counts
4 → 79
Calls
4 calls:
23.0ms
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
23.0ms
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
26.0ms
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
0.0ms
(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
168.0ms
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
173.0ms
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
352.0ms
(cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
414.0ms
(fma (* (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))) (cbrt (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (/ 1.0 (- x 1.0)))

simplify53.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
05281496
117931374
250021321

prune335.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

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

rewrite23.0ms

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 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
4.0ms
(/ 1 (pow x 7))
4.0ms
(/ 1 (pow x 5))
5.0ms
(/ 2.0 (pow x 3))

series208.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(fma 2.0 (/ 1 (pow x 7)) (fma 2.0 (/ 1 (pow x 5)) (/ 2.0 (pow x 3))))
54.0ms
(/ 1 (pow x 7))
48.0ms
(/ 1 (pow x 5))
37.0ms
(/ 2.0 (pow x 3))

simplify51.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0460949
12326816
25001816

prune411.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (pow x 7))
0.1b
(/ (/ 2.0 (* x x)) x)
0.2b
(/ 1 (pow x 5))
0.2b
(/ 2.0 (* x x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
19×div-exp
18×associate-/r*
16×associate-/l*
9×cbrt-undiv
8×div-inv sqr-pow
6×pow-to-exp rec-exp 1-exp pow-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×pow-flip prod-exp cbrt-unprod inv-pow
1×associate-/l/
Counts
4 → 183
Calls
4 calls:
4.0ms
(/ 1 (pow x 7))
6.0ms
(/ (/ 2.0 (* x x)) x)
4.0ms
(/ 1 (pow x 5))
3.0ms
(/ 2.0 (* x x))

series175.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ 1 (pow x 7))
41.0ms
(/ (/ 2.0 (* x x)) x)
43.0ms
(/ 1 (pow x 5))
32.0ms
(/ 2.0 (* x x))

simplify53.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0511914
12528828
25001768

prune395.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0b

regimes86.0ms

Accuracy

99.1% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 10.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03530
13530

end0.0ms

sample586.0ms

Algorithm
intervals
Results
193.0ms1894×body640valid
122.0ms4098×body80valid
75.0ms575×body1280valid
75.0ms939×body320valid
30.0ms496×body160valid