Details

Time bar (total: 2.9s)

sample9.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073
173

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize4.0ms

Local error

Found 1 expressions with local error:

17.1b
(/ x (+ (* x x) 1.0))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg flip3-+ div-exp clear-num flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 31
Calls
1 calls:
6.0ms
(/ x (+ (* x x) 1.0))

series62.0ms

Counts
1 → 3
Calls
1 calls:
62.0ms
(/ x (+ (* x x) 1.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0171215
1589196
21979191
35002186

prune74.0ms

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
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
17.1b
(sqrt (+ (* x x) 1.0))
17.1b
(sqrt (+ (* x x) 1.0))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 sqrt-div div-exp
8×prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 174
Calls
4 calls:
44.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
8.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
5.0ms
(sqrt (+ (* x x) 1.0))
5.0ms
(sqrt (+ (* x x) 1.0))

series226.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
71.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
48.0ms
(sqrt (+ (* x x) 1.0))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06441789
132241573
250021402

prune343.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* x x))
1.9b
(/ x (fma (* 1.0 1.0) 1.0 (pow x 6)))
14.6b
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
25.7b
(* (/ x (fma (* 1.0 1.0) 1.0 (pow x 6))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
117×pow1
36×pow-prod-up
25×add-sqr-sqrt
24×pow-prod-down
23×add-exp-log add-cbrt-cube
22×pow-sqr
20×add-cube-cbrt *-un-lft-identity
19×times-frac
18×pow-plus
14×associate-*l*
13×pow2
10×prod-exp cbrt-unprod
9×add-log-exp
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×associate-+r+ flip3-+ associate-/r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp sum-log *-commutative div-inv
1×+-commutative distribute-rgt-in associate-+r- sub-neg fma-def frac-2neg distribute-lft-in diff-log swap-sqr prod-diff associate-*l/ clear-num
Counts
4 → 153
Calls
4 calls:
12.0ms
(* (* x x) (* x x))
2.0ms
(/ x (fma (* 1.0 1.0) 1.0 (pow x 6)))
18.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
73.0ms
(* (/ x (fma (* 1.0 1.0) 1.0 (pow x 6))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (* x x) (* x x))
238.0ms
(/ x (fma (* 1.0 1.0) 1.0 (pow x 6)))
41.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
130.0ms
(* (/ x (fma (* 1.0 1.0) 1.0 (pow x 6))) (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06261253
129001038
250011006

prune351.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
0.3b
(/ 1 (pow x 5))
0.4b
(/ 1 (pow x 3))
20.3b
(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
59×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
19×associate-/r*
13×fma-neg prod-diff
12×cube-prod div-exp
8×add-cbrt-cube sqr-pow
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l* add-log-exp
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u div-inv
2×cbrt-undiv pow-flip frac-2neg clear-num frac-sub inv-pow
1×sub-neg flip3-- diff-log associate-*r/ un-div-inv flip-- fma-udef
Counts
4 → 182
Calls
4 calls:
13.0ms
(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
4.0ms
(/ 1 (pow x 5))
5.0ms
(/ 1 (pow x 3))
0.0ms
(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

series192.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (/ 1 x) (* 1.0 (/ 1 (pow x 3))))
48.0ms
(/ 1 (pow x 5))
31.0ms
(/ 1 (pow x 3))
44.0ms
(fma 1.0 (/ 1 (pow x 5)) (- (/ 1 x) (* 1.0 (/ 1 (pow x 3)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04691124
12427837
25001831

prune309.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes27.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch81.0ms

Steps
ItersRangePoint
10
13.582308112339199
112933556595576.11
447.21006186250656
10
-8.110240356876969e+23
-16633526390.965715
-3.030132556445137e+19

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03921
13921

end0.0ms

sample217.0ms

Algorithm
intervals
Results
135.0ms8000×body80valid