Details

Time bar (total: 3.9s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms96×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×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×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u 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 hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
8.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series222.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(sqrt (+ x 1.0))
146.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0334508
11222457
25002445

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

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))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
27×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 expm1-log1p-u flip3-+ associate-/r* flip-+ log1p-expm1-u 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 hypot-def div-inv rem-cube-cbrt
Counts
4 → 125
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(pow (sqrt (+ x 1.0)) 3)
11.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
6.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

series278.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
64.0ms
(pow (sqrt (+ x 1.0)) 3)
147.0ms
(/ x (+ 1.0 (cbrt (pow (sqrt (+ x 1.0)) 3))))
31.0ms
(cbrt (pow (sqrt (+ x 1.0)) 3))

simplify54.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0455860
11900759
25002732

prune253.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
29×add-exp-log
12×div-exp
9×prod-exp
8×times-frac add-cbrt-cube associate-/l*
7×add-sqr-sqrt pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
6×unpow-prod-down
5×add-log-exp
3×pow1 expm1-log1p-u frac-add log1p-expm1-u
2×cbrt-undiv unpow2 sqr-pow
1×+-commutative frac-times fma-def frac-2neg flip3-+ associate-*r/ associate-*l/ clear-num associate-/r* sum-log cbrt-unprod flip-+ fma-udef div-inv
Counts
3 → 70
Calls
3 calls:
35.0ms
(+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0)))
11.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
1.0ms
(fma (- 1/2) (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 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))) (/ x (+ (sqrt 1.0) 1.0)))))

series1.0s

Counts
3 → 9
Calls
3 calls:
345.0ms
(+ (* (/ 1/4 1.0) (/ (pow x 3) (pow (+ (sqrt 1.0) 1.0) 3))) (/ x (+ (sqrt 1.0) 1.0)))
180.0ms
(/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2)))
494.0ms
(fma (- 1/2) (/ (pow x 2) (* (sqrt 1.0) (pow (+ (sqrt 1.0) 1.0) 2))) (fma 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))) (/ x (+ (sqrt 1.0) 1.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04241151
121481011
25001995

prune322.0ms

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)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
60×add-sqr-sqrt
52×times-frac
43×sqrt-prod
41×add-cube-cbrt
30×associate-*r*
16×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1 fma-def
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ associate-/r* associate-/r/ flip-+ log1p-expm1-u
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 hypot-def
Counts
4 → 148
Calls
4 calls:
12.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
7.0ms
(+ (sqrt (+ x 1.0)) 1.0)
4.0ms
(sqrt (+ x 1.0))
17.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
309.0ms
(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
42.0ms
(+ (sqrt (+ x 1.0)) 1.0)
36.0ms
(sqrt (+ x 1.0))
137.0ms
(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05531320
123231172
250011139

prune305.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

99.8% (0.0b remaining)

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

bsearch31.0ms

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
153.0ms7999×body80valid
53.0ms2652×body80nan
0.0ms1×body1280valid