Details

Time bar (total: 2.9s)

sample10.0ms

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: 13.6b

localize4.0ms

Local error

Found 1 expressions with local error:

13.6b
(/ x (+ (* x x) 1.0))

rewrite16.0ms

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:
15.0ms
(/ x (+ (* x x) 1.0))

series57.0ms

Counts
1 → 3
Calls
1 calls:
57.0ms
(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0171215
1589196
21979191
35002186

prune71.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b
(/ x (sqrt (+ (* x x) 1.0)))
13.5b
(sqrt (+ (* x x) 1.0))
13.5b
(sqrt (+ (* x x) 1.0))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
166×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
1×associate-/l/
Counts
4 → 272
Calls
4 calls:
41.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
14.0ms
(/ x (sqrt (+ (* x x) 1.0)))
9.0ms
(sqrt (+ (* x x) 1.0))
9.0ms
(sqrt (+ (* x x) 1.0))

series282.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
130.0ms
(/ x (sqrt (+ (* x x) 1.0)))
43.0ms
(sqrt (+ (* x x) 1.0))
51.0ms
(sqrt (+ (* x x) 1.0))

simplify84.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
07933899
130513471
250023383

prune439.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize3.0ms

Local error

Found 1 expressions with local error:

13.6b
(/ x (fma x x 1.0))

rewrite6.0ms

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*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
5.0ms
(/ x (fma x x 1.0))

series71.0ms

Counts
1 → 3
Calls
1 calls:
71.0ms
(/ x (fma x x 1.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0130164
1431151
21442151
35001149

prune58.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
0.1b
(/ 1 (pow x 5))
0.2b
(/ 1 (pow x 3))
19.3b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
1934×times-frac
1320×add-sqr-sqrt
1236×*-un-lft-identity
1171×add-cube-cbrt
1000×prod-diff
650×unpow-prod-down
251×cube-prod
238×sqr-pow
79×cube-mult unpow3
72×div-inv
63×difference-of-squares
25×fma-neg
22×add-exp-log
19×associate-/r*
12×div-exp
8×add-cbrt-cube
7×distribute-lft-out--
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-flip frac-2neg clear-num inv-pow
1×sub-neg flip3-- diff-log frac-sub flip-- fma-udef
Counts
4 → 1250
Calls
4 calls:
0.0ms
(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
8.0ms
(/ 1 (pow x 5))
9.0ms
(/ 1 (pow x 3))
108.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(fma 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3))) (/ 1 x))
51.0ms
(/ 1 (pow x 5))
34.0ms
(/ 1 (pow x 3))
102.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify263.0ms

Algorithm
egg-herbie
Counts
1262 → 1262
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0241132445
1500218251

prune488.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

100% (0.0b remaining)

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

bsearch55.0ms

Steps
ItersRangePoint
10
26.826342714152005
1.350953981158519e+19
3500.8467687195057
8
-40742292820.96068
-15359524.008108458
-24215928678.961597

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0259
1259

end0.0ms

sample243.0ms

Algorithm
intervals
Results
133.0ms8000×body80valid