Details

Time bar (total: 4.2s)

sample50.0ms

Algorithm
intervals
Results
22.0ms775×body80nan
12.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2187
3187

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

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:
3.0ms
(sqrt (- 1.0 (* x x)))
28.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series570.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (- 1.0 (* x x)))
100.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
282.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
127.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify55.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05371057
119211003
25001992

prune347.0ms

Filtered
131 candidates to 109 candidates (83.2%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1.0 x) (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))))
0.3b
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
0.3b
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
0.4b
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
285×sqrt-prod
269×add-sqr-sqrt
232×times-frac
179×*-un-lft-identity
127×add-cube-cbrt
58×associate-*r*
46×associate-*l*
26×difference-of-squares
25×unswap-sqr
21×add-exp-log
20×add-cbrt-cube
16×associate-/l*
13×distribute-lft-out distribute-lft-out--
12×associate-/r*
7×pow1
6×cbrt-undiv div-exp
5×log-div
4×expm1-log1p-u sqrt-undiv sqrt-div prod-exp cbrt-unprod log1p-expm1-u div-inv associate-/l/ add-log-exp
3×log-prod frac-add
2×frac-times frac-2neg flip3-+ associate-*r/ associate-*l/ clear-num flip-+
1×flip3-- sqrt-unprod rem-log-exp pow-prod-down log-pow *-commutative flip--
Counts
4 → 329
Calls
4 calls:
7.0ms
(log (+ (/ 1.0 x) (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))))
13.0ms
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
13.0ms
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
89.0ms
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

series753.0ms

Counts
4 → 12
Calls
4 calls:
330.0ms
(log (+ (/ 1.0 x) (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))))
124.0ms
(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
109.0ms
(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
190.0ms
(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

simplify68.0ms

Algorithm
egg-herbie
Counts
341 → 341
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011614673
150014486

prune839.0ms

Filtered
341 candidates to 203 candidates (59.5%)
Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01714
11714

end0.0ms

sample1.3s

Algorithm
intervals
Results
670.0ms23664×body80nan
287.0ms8000×body80valid