Details

Time bar (total: 5.1s)

sample13.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms96×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
084
184

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
17.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series224.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
30.0ms
(sqrt (+ x 1.0))
147.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0317483
11159435
25001427

prune133.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(pow (sqrt (+ x 1.0)) 3)
0.2b
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
5.9b
(cbrt (pow (sqrt (+ x 1.0)) 3))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
25×add-sqr-sqrt
24×add-cube-cbrt
20×cbrt-prod sqrt-prod
14×unpow-prod-down cube-prod
12×times-frac
9×distribute-lft-out
7×pow1 add-exp-log add-cbrt-cube
6×sqrt-div
4×cube-div flip3-+ associate-/r* flip-+ add-log-exp
3×pow-unpow pow-pow associate-/l*
2×cube-mult cbrt-div sqrt-pow1 pow1/2 unpow3 associate-/r/ sqr-pow
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg pow1/3 div-exp pow-exp clear-num sqrt-pow2 rem-cbrt-cube div-inv rem-cube-cbrt
Counts
4 → 116
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
5.0ms
(pow (sqrt (+ x 1.0)) 3)
41.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
6.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

series282.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (+ x 1.0))
63.0ms
(pow (sqrt (+ x 1.0)) 3)
146.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
36.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify56.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0438828
11823728
25002713

prune221.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
0.0b
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
0.0b
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
7.2b
(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

rewrite320.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log
22×associate-*r/
21×frac-add
20×add-log-exp
12×div-exp frac-sub
10×*-un-lft-identity
9×prod-exp add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt times-frac associate-/l*
7×pow-to-exp flip3-+ pow-exp sum-log flip-+
6×unpow-prod-down
4×pow1 frac-times flip3-- associate-*l/ flip--
3×diff-log
2×cbrt-undiv +-commutative sub-neg associate-+r+ unpow2 sqr-pow
1×associate-+r- associate-+l+ frac-2neg clear-num associate-/r* cbrt-unprod div-inv distribute-lft-out
Counts
4 → 102
Calls
4 calls:
34.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
15.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
238.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
30.0ms
(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
478.0ms
(+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2)))))
180.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
523.0ms
(+ (+ (/ x (+ (sqrt 1.0) 1.0)) (* 1/8 (/ (pow x 3) (* (pow (sqrt 1.0) 3) (pow (+ (sqrt 1.0) 1.0) 2))))) (- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))))))
494.0ms
(- (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))))

simplify169.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (136.0ms)

IterNodesCost
07893619
146343468
250023456

prune494.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
0.0b
(+ (sqrt (+ x 1.0)) 1.0)
0.0b
(sqrt (+ x 1.0))
0.2b
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
21.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
17.0ms
(+ (sqrt (+ x 1.0)) 1.0)
4.0ms
(sqrt (+ x 1.0))
53.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series519.0ms

Counts
4 → 12
Calls
4 calls:
296.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
48.0ms
(+ (sqrt (+ x 1.0)) 1.0)
31.0ms
(sqrt (+ x 1.0))
143.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05281280
122421133
250011106

prune258.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes20.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.4b

bsearch37.0ms

Steps
ItersRangePoint
9
1.560051953962792e-13
7.712829756242493e-08
8.626548691723187e-11

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02013
12013

end0.0ms

sample319.0ms

Algorithm
intervals
Results
152.0ms7999×body80valid
49.0ms2652×body80nan
0.0ms1×body1280valid