Details

Time bar (total: 1.8s)

sample10.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

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: 15.7b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.7b
(/ 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))

series59.0ms

Counts
1 → 3
Calls
1 calls:
59.0ms
(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0165210
1555195
21825192
35001192

prune57.0ms

Filtered
32 candidates to 26 candidates (81.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New29332
Fresh000
Picked101
Done000
Total30333

Merged error: 0b

Counts
33 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b
(/ x (sqrt (+ (* x x) 1.0)))
15.7b
(sqrt (+ (* x x) 1.0))
15.7b
(sqrt (+ (* x x) 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
30×sqrt-prod
12×associate-/r*
10×add-exp-log
8×pow1 sqrt-div add-cbrt-cube
6×associate-/l*
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp
2×cbrt-undiv rem-sqrt-square frac-2neg clear-num div-inv
1×rec-exp 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
9.0ms
(/ 1 (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))

series285.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
121.0ms
(/ x (sqrt (+ (* x x) 1.0)))
46.0ms
(sqrt (+ (* x x) 1.0))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0388966
11519889
25001850

prune187.0ms

Filtered
130 candidates to 84 candidates (64.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1300130
Fresh022
Picked011
Done000
Total1303133

Merged error: 0b

Counts
133 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

3.0b
(/ x (+ (neg (* 1.0 1.0)) (pow x 4)))
20.4b
(* (/ x (+ (neg (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
20×add-cube-cbrt
18×associate-*l*
9×add-exp-log add-cbrt-cube
7×distribute-lft-out
4×pow1 associate-*r* associate-/r* associate-/r/
3×associate-/l*
2×cbrt-undiv distribute-rgt-in frac-times sub-neg flip3-- distribute-lft-in flip3-+ associate-*r/ div-exp prod-exp flip-- cbrt-unprod flip-+ div-inv add-log-exp unswap-sqr
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative difference-of-squares
Counts
2 → 79
Calls
2 calls:
10.0ms
(/ x (+ (neg (* 1.0 1.0)) (pow x 4)))
15.0ms
(* (/ x (+ (neg (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

series226.0ms

Counts
2 → 6
Calls
2 calls:
125.0ms
(/ x (+ (neg (* 1.0 1.0)) (pow x 4)))
101.0ms
(* (/ x (+ (neg (* 1.0 1.0)) (pow x 4))) (- (* x x) 1.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0427860
11887778
25002745

prune153.0ms

Filtered
85 candidates to 63 candidates (74.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New85085
Fresh011
Picked011
Done011
Total85388

Merged error: 0b

Counts
88 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1 (pow x 5))
0.3b
(/ 1 (pow x 3))
22.7b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
195×add-sqr-sqrt
173×times-frac
111×*-un-lft-identity
63×difference-of-squares
56×unpow-prod-down
46×add-cube-cbrt
40×sqr-pow
26×cube-prod
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 div-inv associate-/l*
5×add-log-exp
4×cube-mult unpow3
3×pow1
2×cbrt-undiv pow-flip frac-2neg clear-num inv-pow
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 209
Calls
3 calls:
5.0ms
(/ 1 (pow x 5))
6.0ms
(/ 1 (pow x 3))
48.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(/ 1 (pow x 5))
33.0ms
(/ 1 (pow x 3))
94.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify64.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05461617
120351364
250011364

prune198.0ms

Filtered
218 candidates to 78 candidates (35.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2180218
Fresh000
Picked011
Done022
Total2183221

Merged error: 0b

Counts
221 → 3

regimes23.0ms

bsearch2.0ms

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