Details

Time bar (total: 5.0s)

sample47.0ms

Algorithm
intervals
Results
23.0ms863×body80nan
9.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2167

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
33×times-frac
28×add-sqr-sqrt
24×add-cube-cbrt
16×sqrt-prod
8×log-prod distribute-lft-out
7×associate-/l*
6×add-exp-log
5×add-cbrt-cube div-inv add-log-exp
4×pow1 difference-of-squares
3×log-div associate-/r*
2×distribute-rgt-out flip3-+ sqrt-div frac-add flip-+ associate-/l/
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp rem-log-exp clear-num sum-log log-pow flip--
Counts
3 → 82
Calls
3 calls:
22.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
24.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series510.0ms

Counts
3 → 9
Calls
3 calls:
112.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
121.0ms
(/ (sqrt (- 1.0 (* x x))) x)
276.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify54.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0460892
11594844
25001822

prune222.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1.0 x) (* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
0.3b
(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x))
0.3b
(/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.5b
(* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
164×times-frac
146×sqrt-prod
103×cbrt-prod
94×add-cube-cbrt *-un-lft-identity
64×associate-*r*
33×add-exp-log
22×add-cbrt-cube
21×unswap-sqr
14×cbrt-div sqrt-div
13×difference-of-squares
12×associate-/r*
11×associate-/l*
10×cbrt-undiv div-exp associate-*l* associate-/l/
9×prod-exp cbrt-unprod
7×pow1 flip3-- flip--
6×frac-times
5×log-div
4×associate-*r/ associate-*l/ div-inv add-log-exp
3×log-prod frac-add
2×frac-2neg clear-num
1×flip3-+ rem-log-exp pow-prod-down log-pow *-commutative flip-+
Counts
4 → 261
Calls
4 calls:
6.0ms
(log (+ (/ 1.0 x) (* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
10.0ms
(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x))
11.0ms
(/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x))
52.0ms
(* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
283.0ms
(log (+ (/ 1.0 x) (* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
131.0ms
(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x))
126.0ms
(/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x))
120.0ms
(* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

simplify71.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012715196
150014914

prune872.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (sqrt x)) (cbrt (sqrt x)))
0.7b
(cbrt (sqrt x))
0.7b
(cbrt (sqrt x))
0.7b
(cbrt (sqrt x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
58×cbrt-prod
44×add-sqr-sqrt
29×sqrt-prod
22×add-cube-cbrt *-un-lft-identity
11×pow1 swap-sqr
9×pow1/3 associate-*r* associate-*l* unswap-sqr
6×add-exp-log
4×add-cbrt-cube add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
8.0ms
(* (cbrt (sqrt x)) (cbrt (sqrt x)))
1.0ms
(cbrt (sqrt x))
1.0ms
(cbrt (sqrt x))
1.0ms
(cbrt (sqrt x))

series597.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (cbrt (sqrt x)) (cbrt (sqrt x)))
148.0ms
(cbrt (sqrt x))
148.0ms
(cbrt (sqrt x))
148.0ms
(cbrt (sqrt x))

simplify103.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0148689
1554642
23053585
35001558

prune385.0ms

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
02631
12631

end0.0ms

sample1.3s

Algorithm
intervals
Results
660.0ms24269×body80nan
276.0ms8000×body80valid