Details

Time bar (total: 3.7s)

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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) 1.0)
15.6b
(/ x (+ (* x x) 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 45
Calls
2 calls:
4.0ms
(+ (* x x) 1.0)
5.0ms
(/ x (+ (* x x) 1.0))

series119.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(+ (* x x) 1.0)
66.0ms
(/ x (+ (* x x) 1.0))

simplify115.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0205273
1756247
23230239
35002237

prune98.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

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)))
15.6b
(sqrt (+ (* x x) 1.0))
15.6b
(sqrt (+ (* x x) 1.0))

rewrite47.0ms

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:
18.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
6.0ms
(/ x (sqrt (+ (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series278.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
123.0ms
(/ x (sqrt (+ (* x x) 1.0)))
49.0ms
(sqrt (+ (* x x) 1.0))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify87.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07933897
130573471
250013383

prune459.0ms

Filtered
284 candidates to 160 candidates (56.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
13.4b
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
15.6b
(sqrt (+ (* x x) 1.0))
20.7b
(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
9×add-log-exp
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×associate-+r+ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def
1×cbrt-undiv +-commutative associate-+r- sub-neg sqrt-undiv hypot-udef fma-def frac-2neg diff-log div-exp prod-diff clear-num div-inv
Counts
4 → 99
Calls
4 calls:
12.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
17.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
14.0ms
(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

series435.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
47.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
44.0ms
(sqrt (+ (* x x) 1.0))
262.0ms
(/ (hypot (pow 1.0 3/2) (pow x 3)) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04211548
115581415
250011380

prune418.0ms

Filtered
111 candidates to 87 candidates (78.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (pow x 5))
0.4b
(/ 1 (pow x 3))
20.5b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite223.0ms

Algorithm
rewrite-expression-head
Rules
1934×times-frac
1319×add-sqr-sqrt
1235×*-un-lft-identity
1170×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
21×add-exp-log
19×associate-/r*
12×div-exp
7×add-cbrt-cube distribute-lft-out--
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
5×add-log-exp
3×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--
Counts
3 → 1240
Calls
3 calls:
5.0ms
(/ 1 (pow x 5))
6.0ms
(/ 1 (pow x 3))
76.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series181.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(/ 1 (pow x 5))
32.0ms
(/ 1 (pow x 3))
99.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify271.0ms

Algorithm
egg-herbie
Counts
1249 → 1249
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0238131548
1500118062

prune450.0ms

Filtered
1249 candidates to 124 candidates (9.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 24.2b

bsearch87.0ms

Steps
ItersRangePoint
10
4.9177062248324165e-05
42925490.781275615
764.6675213818143
9
-234806929230.2476
-1816.595590764893
-14917877722.165144

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04125
14125

end0.0ms

sample223.0ms

Algorithm
intervals
Results
136.0ms8000×body80valid