Details

Time bar (total: 12.2s)

sample67.0ms

Algorithm
intervals
Results
34.0ms88×body1280valid
12.0ms53×body640valid
7.0ms26×body2560valid
3.0ms21×body320valid
2.0ms58×body80valid
1.0ms10×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
7×add-cube-cbrt
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod fma-def flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow hypot-def
Counts
4 → 66
Calls
4 calls:
3.0ms
(+ (* x x) 1.0)
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series306.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (* x x) 1.0)
56.0ms
(+ x (sqrt (+ (* x x) 1.0)))
173.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0357480
11262435
25002412

prune216.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv expm1-log1p-u associate-*r/ pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 272
Calls
1 calls:
74.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series132.0ms

Counts
1 → 3
Calls
1 calls:
132.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify95.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07291769
138381380
250031380

prune372.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0.0625) (pow x 5))
0.8b
(/ 0.125 (pow x 3))
14.6b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.3b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite833.0ms

Algorithm
rewrite-expression-head
Rules
2802×times-frac
2496×add-sqr-sqrt
1944×*-un-lft-identity
1522×prod-diff
1510×add-cube-cbrt
965×associate--r+
652×unpow-prod-down
339×distribute-rgt-neg-in
330×difference-of-squares
297×distribute-lft-neg-in
272×sqr-pow
149×cube-prod
134×distribute-lft-out--
104×div-inv
99×neg-mul-1
49×cube-mult unpow3
40×fma-neg
19×associate-/r*
15×add-exp-log
13×associate-/l*
12×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 1793
Calls
4 calls:
7.0ms
(/ (- 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
258.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
343.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (- 0.0625) (pow x 5))
35.0ms
(/ 0.125 (pow x 3))
191.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
54.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify412.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0500248078

prune6.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.6b
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
3×pow1 add-exp-log log-prod fma-def
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative rem-log-exp sum-log log-pow
Counts
2 → 32
Calls
2 calls:
2.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
2.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

series410.0ms

Counts
2 → 6
Calls
2 calls:
127.0ms
(+ x (* (sqrt 1) (hypot x (sqrt 1.0))))
282.0ms
(log (+ x (* (sqrt 1) (hypot x (sqrt 1.0)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0255366
1909318
23872309
35001304

prune103.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.8b

bsearch82.0ms

Steps
ItersRangePoint
10
5.968040026638966e-05
117627206.70733242
0.0009763026979395131
10
-64880754058.88788
-2.651420353119469e-05
-0.9989549344709008

simplify6.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.9s

Algorithm
intervals
Results
976.0ms2398×body1280valid
364.0ms1535×body640valid
222.0ms806×body2560valid
105.0ms761×body320valid
68.0ms2126×body80valid
29.0ms374×body160valid