Details

Time bar (total: 6.1s)

sample67.0ms

Algorithm
intervals
Results
18.0ms558×body80nan
17.0ms277×body160nan
10.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
30.3b
(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 52
Calls
3 calls:
8.0ms
(+ x (sqrt (- (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series310.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(+ x (sqrt (- (* x x) 1.0)))
189.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
53.0ms
(sqrt (- (* x x) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0339436
11140401
25001389

prune155.0ms

Filtered
61 candidates to 53 candidates (86.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
9×add-cube-cbrt associate-*r*
8×pow1
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×expm1-log1p-u log-prod flip3-- fma-def pow-prod-down flip-- log1p-expm1-u
2×log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 76
Calls
3 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
30.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series639.0ms

Counts
3 → 9
Calls
3 calls:
165.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
281.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
193.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04671012
11665907
25001894

prune254.0ms

Filtered
85 candidates to 69 candidates (81.2%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
0.2b
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
0.2b
(/ (pow (sqrt 1.0) 4) (pow x 4))
0.9b
(/ (* 1/4 1.0) (pow x 2))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
98×add-sqr-sqrt
87×unpow-prod-down times-frac
82×add-cube-cbrt
48×prod-diff
33×log-pow
31×pow1
29×add-exp-log
24×sqrt-prod distribute-lft-out--
21×sqr-pow
20×associate--l+
16×log-prod
15×div-exp associate-/r*
13×associate--r+
11×add-cbrt-cube associate-/l*
8×pow-to-exp pow-exp difference-of-squares
6×pow-flip fma-neg inv-pow add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv diff-log prod-exp div-inv
2×sub-neg frac-2neg clear-num unpow2
1×associate--l- log-div flip3-- flip-- cbrt-unprod fma-udef associate--r-
Counts
4 → 252
Calls
4 calls:
0.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
33.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
8.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
5.0ms
(/ (* 1/4 1.0) (pow x 2))

series471.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))
154.0ms
(- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (/ 1 x)))
103.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
31.0ms
(/ (* 1/4 1.0) (pow x 2))

simplify106.0ms

Algorithm
egg-herbie
Counts
264 → 264
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
08293752
133942759
250022659

prune705.0ms

Filtered
264 candidates to 140 candidates (53.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1 x))
0.2b
(/ (pow (sqrt 1.0) 4) (pow x 4))
0.2b
(- (- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (sqrt (/ 1 x)))) (log (sqrt (/ 1 x))))
0.9b
(/ (* 1/4 1.0) (pow x 2))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
265×*-un-lft-identity
153×log-pow
150×add-sqr-sqrt
140×prod-diff distribute-lft-out--
127×pow1
110×add-cube-cbrt
98×times-frac
88×associate--l+
87×unpow-prod-down
51×sqrt-pow1
50×sqrt-prod
29×add-exp-log
21×sqr-pow
19×log-prod
18×difference-of-squares
17×pow-flip pow1/2 inv-pow
16×associate--r+
15×div-exp associate-/r*
11×add-cbrt-cube associate-/l*
10×fma-neg
8×pow-to-exp pow-exp
7×add-log-exp
6×diff-log
4×expm1-log1p-u log1p-expm1-u div-inv
3×cbrt-undiv sub-neg rem-sqrt-square sqrt-div prod-exp
2×log-div frac-2neg clear-num unpow2 associate--r-
1×associate--l- flip3-- flip-- cbrt-unprod
Counts
4 → 383
Calls
4 calls:
4.0ms
(sqrt (/ 1 x))
8.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
180.0ms
(- (- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (sqrt (/ 1 x)))) (log (sqrt (/ 1 x))))
5.0ms
(/ (* 1/4 1.0) (pow x 2))

series312.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(sqrt (/ 1 x))
108.0ms
(/ (pow (sqrt 1.0) 4) (pow x 4))
151.0ms
(- (- (- (log 2) (fma 3/32 (/ (pow (sqrt 1.0) 4) (pow x 4)) (/ (* 1/4 1.0) (pow x 2)))) (log (sqrt (/ 1 x)))) (log (sqrt (/ 1 x))))
28.0ms
(/ (* 1/4 1.0) (pow x 2))

simplify145.0ms

Algorithm
egg-herbie
Counts
395 → 395
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
010206725
140294192
250013976

prune1.2s

Filtered
395 candidates to 193 candidates (48.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.3s

Algorithm
intervals
Results
349.0ms7744×body160nan
339.0ms16599×body80nan
221.0ms8000×body80valid