Details

Time bar (total: 3.8s)

sample51.0ms

Algorithm
intervals
Results
23.0ms773×body80nan
12.0ms256×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

localize10.0ms

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)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
42×times-frac
39×add-sqr-sqrt
33×add-cube-cbrt
20×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube div-inv add-log-exp
5×difference-of-squares
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 119
Calls
4 calls:
20.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
3.0ms
(sqrt (- 1.0 (* x x)))
19.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series588.0ms

Counts
4 → 12
Calls
4 calls:
292.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
63.0ms
(sqrt (- 1.0 (* x x)))
104.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
130.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify55.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
05371057
119211003
25001992

prune351.0ms

Filtered
131 candidates to 109 candidates (83.2%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1301131
Fresh000
Picked101
Done000
Total1311132

Merged error: 0b

Counts
132 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))
0.2b
(/ 1 (sqrt x))
0.2b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
0.5b
(* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
190×add-sqr-sqrt
170×times-frac
148×sqrt-prod
107×*-un-lft-identity
96×add-cube-cbrt
46×associate-*r*
32×add-exp-log
25×unswap-sqr
22×associate-*l*
20×add-cbrt-cube
13×fma-def difference-of-squares
12×associate-/r*
11×div-exp
10×associate-/l*
8×pow1 prod-exp
6×cbrt-undiv add-log-exp
5×div-inv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×rec-exp pow-flip 1-exp frac-add
2×frac-times frac-2neg sqrt-div associate-*r/ associate-*l/ clear-num associate-/l/
1×+-commutative sqrt-undiv flip3-- sqrt-pow1 flip3-+ pow1/2 pow-prod-down sum-log *-commutative flip-- flip-+ distribute-lft-out inv-pow
Counts
4 → 268
Calls
4 calls:
7.0ms
(+ (/ 1.0 x) (* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))
4.0ms
(/ 1 (sqrt x))
7.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
31.0ms
(* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(+ (/ 1.0 x) (* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))
32.0ms
(/ 1 (sqrt x))
68.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
116.0ms
(* (/ 1 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))

simplify112.0ms

Algorithm
egg-herbie
Counts
280 → 280
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
09302805
145972505
250012482

prune766.0ms

Filtered
280 candidates to 163 candidates (58.2%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New2800280
Fresh000
Picked011
Done000
Total2801281

Merged error: 0b

Counts
281 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01711
11711

end0.0ms

sample1.4s

Algorithm
intervals
Results
711.0ms23979×body80nan
283.0ms8000×body80valid