Details

Time bar (total: 2.3s)

sample9.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163

prune1.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.8b

Counts
2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

14.8b
(/ x (+ (* 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*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
5.0ms
(/ x (+ (* x x) 1.0))

series53.0ms

Counts
1 → 3
Calls
1 calls:
53.0ms
(/ x (+ (* x x) 1.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0165210
1555195
21825192
35001192

prune59.0ms

Filtered
32 candidates to 26 candidates (81.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New29332
Fresh000
Picked011
Done000
Total29433

Merged error: 0b

Counts
33 → 4

localize8.0ms

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)))
14.7b
(sqrt (+ (* x x) 1.0))
14.7b
(sqrt (+ (* x x) 1.0))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×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 div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 262
Calls
4 calls:
15.0ms
(/ (/ 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))

series258.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
119.0ms
(/ x (sqrt (+ (* x x) 1.0)))
40.0ms
(sqrt (+ (* x x) 1.0))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify85.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
07743878
129623482
250023411

prune317.0ms

Filtered
274 candidates to 147 candidates (53.6%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2740274
Fresh022
Picked011
Done011
Total2744278

Merged error: 0b

Counts
278 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (neg (* 1.0 1.0)) (pow x 4))
0.0b
(- (* x x) 1.0)
2.8b
(/ x (+ (neg (* 1.0 1.0)) (pow x 4)))
18.8b
(* (/ x (+ (neg (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
29×add-sqr-sqrt
25×times-frac
22×add-cube-cbrt
18×associate-*l*
11×add-exp-log add-cbrt-cube
10×add-log-exp
8×distribute-lft-out
6×pow1
4×associate-*r* associate-/r* associate-/r/
3×sub-neg flip3-- flip3-+ flip-- flip-+ associate-/l*
2×cbrt-undiv distribute-rgt-in frac-times distribute-lft-in associate-*r/ div-exp prod-exp sum-log cbrt-unprod div-inv difference-of-squares unswap-sqr
1×+-commutative neg-sub0 associate-+l- frac-2neg diff-log pow-prod-down neg-log associate-*l/ clear-num *-commutative
Counts
4 → 106
Calls
4 calls:
6.0ms
(+ (neg (* 1.0 1.0)) (pow x 4))
4.0ms
(- (* x x) 1.0)
7.0ms
(/ x (+ (neg (* 1.0 1.0)) (pow x 4)))
14.0ms
(* (/ x (+ (neg (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

series339.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (neg (* 1.0 1.0)) (pow x 4))
42.0ms
(- (* x x) 1.0)
124.0ms
(/ x (+ (neg (* 1.0 1.0)) (pow x 4)))
102.0ms
(* (/ x (+ (neg (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04621022
12313920
25001900

prune200.0ms

Filtered
118 candidates to 85 candidates (72.0%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1180118
Fresh011
Picked011
Done022
Total1184122

Merged error: 0b

Counts
122 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
0.1b
(/ 1 (pow x 5))
0.1b
(/ 1 (pow x 3))
19.4b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
196×add-sqr-sqrt
173×times-frac
112×*-un-lft-identity
63×difference-of-squares
56×unpow-prod-down
47×add-cube-cbrt
40×sqr-pow
26×cube-prod
22×add-exp-log
19×associate-/r*
12×div-exp
8×add-cbrt-cube add-log-exp
7×distribute-lft-out--
6×pow-to-exp rec-exp 1-exp pow-exp div-inv associate-/l*
4×pow1 cube-mult associate-+l+ unpow3
3×sub-neg associate-*r/ frac-add
2×cbrt-undiv distribute-rgt-in flip3-- pow-flip frac-2neg distribute-lft-in clear-num frac-sub flip-- inv-pow
1×+-commutative flip3-+ diff-log sum-log flip-+
Counts
4 → 227
Calls
4 calls:
51.0ms
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
5.0ms
(/ 1 (pow x 5))
5.0ms
(/ 1 (pow x 3))
44.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
41.0ms
(/ 1 (pow x 5))
35.0ms
(/ 1 (pow x 3))
92.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify91.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
06871905
128791620
250011619

prune245.0ms

Filtered
239 candidates to 92 candidates (38.5%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New2390239
Fresh000
Picked011
Done033
Total2394243

Merged error: 0b

Counts
243 → 4

regimes52.0ms

bsearch2.0ms

Profiling

Loading profile data...