Details

Time bar (total: 12.1s)

sample52.0ms

Algorithm
intervals
Results
25.0ms809×body80nan
9.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0127
1167
2187
3187

prune2.0ms

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: 0.0b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
408×add-sqr-sqrt
378×frac-add
373×associate-/l*
285×*-un-lft-identity
230×sqrt-prod
191×log-div
183×associate-/r*
177×add-cube-cbrt
115×difference-of-squares
61×frac-2neg clear-num
60×times-frac
46×distribute-lft-out--
40×sqrt-div
38×associate-/l/
23×swap-sqr associate-*l* *-commutative unswap-sqr
20×flip3-- flip--
13×fma-def
8×log-prod distribute-lft-out
7×add-exp-log
6×pow1 add-cbrt-cube div-inv add-log-exp
4×expm1-log1p-u log1p-expm1-u
2×distribute-rgt-out flip3-+ flip-+
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-pow1 pow1/2 div-exp rem-log-exp sum-log log-pow
Counts
4 → 525
Calls
4 calls:
52.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
15.0ms
(sqrt (- 1.0 (* x x)))
40.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
12.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series594.0ms

Counts
4 → 12
Calls
4 calls:
295.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
60.0ms
(sqrt (- 1.0 (* x x)))
101.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
137.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify118.0ms

Algorithm
egg-herbie
Counts
537 → 537
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
021938432
150018259

prune1.0s

Filtered
537 candidates to 295 candidates (54.9%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New5361537
Fresh000
Picked101
Done000
Total5371538

Merged error: 0b

Counts
538 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt x))
0.2b
(/ 1.0 (sqrt x))
0.2b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.5b
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

rewrite819.0ms

Algorithm
rewrite-expression-head
Rules
4572×associate-/r*
4173×add-sqr-sqrt
3992×sqrt-prod
3856×associate-/l*
3744×frac-add
3480×frac-times
3199×*-un-lft-identity
2527×add-cube-cbrt
815×difference-of-squares
762×frac-2neg clear-num
326×distribute-lft-out--
314×sqrt-div associate-/l/
290×associate-*r/
185×associate-*l*
168×unswap-sqr
164×*-commutative
163×swap-sqr
157×flip3-- flip--
152×times-frac
21×add-exp-log
15×add-cbrt-cube
13×flip3-+ associate-*r* flip-+
12×associate-*l/
9×distribute-lft-out
8×pow1
6×div-exp div-inv
4×cbrt-undiv expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×pow-flip
2×+-commutative distribute-rgt-in rec-exp distribute-lft-in 1-exp cbrt-unprod
1×sqrt-undiv distribute-rgt-out sqrt-pow1 pow1/2 pow-prod-down inv-pow
Counts
4 → 4045
Calls
4 calls:
4.0ms
(/ 1 (sqrt x))
4.0ms
(/ 1.0 (sqrt x))
13.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
209.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ 1 (sqrt x))
38.0ms
(/ 1.0 (sqrt x))
70.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
206.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

simplify892.0ms

Algorithm
egg-herbie
Counts
4057 → 4057
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
05003104097

prune6.5s

Filtered
4057 candidates to 1426 candidates (35.1%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New405704057
Fresh000
Picked011
Done000
Total405714058

Merged error: 0b

Counts
4058 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample1.5s

Algorithm
intervals
Results
870.0ms23458×body80nan
296.0ms8000×body80valid