Details

Time bar (total: 3.7s)

sample51.0ms

Algorithm
intervals
Results
25.0ms809×body80nan
9.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2187
3187

prune5.0ms

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:
19.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
3.0ms
(sqrt (- 1.0 (* x x)))
20.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series788.0ms

Counts
4 → 12
Calls
4 calls:
491.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
60.0ms
(sqrt (- 1.0 (* x x)))
103.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
133.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify52.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
05371057
119211003
25001992

prune346.0ms

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

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))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
116×times-frac
105×add-sqr-sqrt
102×*-un-lft-identity
95×sqrt-prod
82×add-cube-cbrt
22×associate-*l*
21×add-exp-log
18×associate-/r*
15×add-cbrt-cube
13×associate-*r* associate-/l*
9×distribute-lft-out
8×pow1
7×difference-of-squares
6×div-exp div-inv
5×unswap-sqr
4×cbrt-undiv expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×frac-times pow-flip frac-2neg associate-*r/ clear-num
2×rec-exp flip3-+ sqrt-div 1-exp frac-add cbrt-unprod flip-+ associate-/l/
1×distribute-rgt-in sqrt-undiv distribute-rgt-out flip3-- distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 226
Calls
4 calls:
4.0ms
(/ 1 (sqrt x))
4.0ms
(/ 1.0 (sqrt x))
7.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
56.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

series327.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1 (sqrt x))
42.0ms
(/ 1.0 (sqrt x))
64.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))
194.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))

simplify93.0ms

Algorithm
egg-herbie
Counts
238 → 238
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08362199
139531977
250021907

prune489.0ms

Filtered
238 candidates to 148 candidates (62.2%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New2380238
Fresh000
Picked011
Done000
Total2381239

Merged error: 0b

Counts
239 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample1.4s

Algorithm
intervals
Results
715.0ms23458×body80nan
286.0ms8000×body80valid