Details

Time bar (total: 3.5s)

sample21.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
4.0ms102×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))))

rewrite35.0ms

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:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
18.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series218.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(sqrt (+ x 1.0))
142.0ms
(/ 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

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
34×add-sqr-sqrt
26×times-frac
24×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×expm1-log1p-u flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+ log1p-expm1-u
3×fma-def associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative hypot-def inv-pow
Counts
4 → 118
Calls
4 calls:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
5.0ms
(sqrt (+ x 1.0))
17.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
43.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(sqrt (+ x 1.0))
105.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
144.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0472857
12046741
25002696

prune221.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.2b
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
14.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
4.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))

series492.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
216.0ms
(/ x (+ 1.0 (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))))
89.0ms
(cbrt (+ x 1.0))
89.0ms
(cbrt (+ x 1.0))

simplify80.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07071346
131771264
250011230

prune324.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0)
0.2b
(/ x (fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0))
0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
9×times-frac
8×cbrt-prod
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u cbrt-div log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×flip3-+ pow1/3 flip-+ distribute-lft-out
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 71
Calls
4 calls:
0.0ms
(fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0)
2.0ms
(/ x (fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))

series502.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0)
220.0ms
(/ x (fma (sqrt (cbrt (+ x 1.0))) (fabs (cbrt (+ x 1.0))) 1.0))
88.0ms
(cbrt (+ x 1.0))
89.0ms
(cbrt (+ x 1.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06101092
126161015
25001999

prune286.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084
184

end0.0ms

sample532.0ms

Algorithm
intervals
Results
312.0ms7999×body80valid
96.0ms2604×body80nan
0.0ms1×body1280valid