Details

Time bar (total: 5.9s)

sample30.0ms

Algorithm
intervals
Results
6.0ms62×body640valid
6.0ms275×body80nan
4.0ms140×body80valid
3.0ms27×body1280valid
1.0ms14×body320valid
1.0ms13×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
66.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
138.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify245.0ms

Algorithm
egg-herbie
Counts
770 → 770
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
0153825022
1427218390
2500118355

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
62×*-un-lft-identity
56×add-sqr-sqrt
42×prod-diff
37×add-cube-cbrt
18×add-exp-log add-cbrt-cube
10×distribute-lft-out
9×pow1
7×fma-neg associate-*r*
6×sqrt-div associate-*r/ associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out--
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative hypot-def div-inv associate-/l*
Counts
4 → 151
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
51.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
16.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
27.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series430.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ x 1.0))
264.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
68.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify87.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06361812
129451369
250021271

prune341.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 17.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))
0.3b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.5b
(* (sqrt x) (sqrt x))
2.9b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
44×sqrt-prod
36×*-un-lft-identity
34×pow1
22×add-cube-cbrt
19×swap-sqr
16×sqrt-pow1 pow1/2
13×add-exp-log associate-*r* associate-*l* add-cbrt-cube
12×sqrt-div
10×pow-prod-up
8×unswap-sqr
6×flip3-+ pow-prod-down pow-sqr flip-+ distribute-lft-out add-log-exp
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×times-frac prod-exp associate-/r* cbrt-unprod
2×cbrt-undiv pow2 flip3-- pow-plus sqrt-unprod div-exp associate-*l/ rem-square-sqrt *-commutative flip-- associate-/l/
1×sub-neg frac-2neg fma-neg diff-log prod-diff clear-num div-inv associate-/l* difference-of-squares
Counts
4 → 157
Calls
4 calls:
23.0ms
(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))
24.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
7.0ms
(* (sqrt x) (sqrt x))
12.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(/ (* 1.0 (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))
21.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
15.0ms
(* (sqrt x) (sqrt x))
14.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

simplify94.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
05861239
13124990
25003919

prune349.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0))))
0.1b
(* x (sqrt (+ x 1.0)))
0.4b
(/ (* 1.0 (log (* (exp 1.0) (exp (- x x))))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt
9×sqrt-prod
7×pow1 associate-*r*
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×times-frac associate-*l* associate-/r*
2×cbrt-undiv flip3-+ associate-*r/ div-exp prod-exp cbrt-unprod flip-+ distribute-lft-out unswap-sqr
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down clear-num *-commutative fma-udef hypot-def div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
0.0ms
(fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0))))
11.0ms
(* x (sqrt (+ x 1.0)))
29.0ms
(/ (* 1.0 (log (* (exp 1.0) (exp (- x x))))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))

series611.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
137.0ms
(fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0))))
76.0ms
(* x (sqrt (+ x 1.0)))
361.0ms
(/ (* 1.0 (log (* (exp 1.0) (exp (- x x))))) (fma (sqrt x) (+ x 1.0) (* x (sqrt (+ x 1.0)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0512881
12375697
25001658

prune296.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

regimes60.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02019
12019

end0.0ms

sample1.0s

Algorithm
intervals
Results
346.0ms1174×body1280valid
184.0ms1782×body640valid
164.0ms7968×body80nan
108.0ms4128×body80valid
44.0ms607×body320valid
15.0ms309×body160valid