Details

Time bar (total: 21.6s)

sample332.0ms

Algorithm
intervals
Results
271.0ms3513×body80valid

simplify913.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (181.0ms)

IterNodesCost
031103
190103
236466
3180354
done500054

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
120×times-frac
89×add-cube-cbrt *-un-lft-identity
40×add-exp-log add-cbrt-cube
39×swap-sqr associate-*r* associate-*l*
26×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×add-log-exp
3×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ sqrt-prod pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 214
Calls
4 calls:
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
16.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms
(sqrt PI)

series75.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify710.0ms

Counts
224 → 224
Iterations

Useful iterations: done (703.0ms)

IterNodesCost
01463221
14212898
215932387
done50002378

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
52×times-frac
44×unpow-prod-down
43×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
38×cube-prod
24×add-exp-log
16×add-cbrt-cube
13×pow-exp
9×pow-unpow
8×pow1 div-exp
7×rem-cube-cbrt
6×div-inv
5×pow-to-exp sqr-pow
4×cbrt-undiv add-log-exp
3×cube-div cube-mult pow-pow unpow3 prod-exp sqrt-prod
2×unpow2
1×rem-sqrt-square sqrt-pow1 pow1/2 cbrt-unprod
Counts
4 → 155
Calls
4 calls:
6.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series129.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
32.0ms
(pow (/ 1.0 (fabs x)) 3)
39.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.1s

Counts
165 → 165
Iterations

Useful iterations: 2 (346.0ms)

IterNodesCost
01882052
15531821
221091480
done50001480

prune638.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (/ 3.0 4.0) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
82×add-exp-log
54×times-frac
51×add-sqr-sqrt
50×add-cube-cbrt *-un-lft-identity
39×unpow-prod-down cube-prod
36×prod-exp
32×associate-*r*
28×add-cbrt-cube
23×div-exp
14×pow-exp
9×cbrt-unprod
7×pow1 pow-to-exp
6×cbrt-undiv cube-div pow-unpow div-inv
5×frac-times associate-*l/
4×add-log-exp rem-cube-cbrt
3×cube-mult unpow3 associate-*r/ sqrt-prod sqr-pow
2×pow-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 178
Calls
4 calls:
33.0ms
(* (* (/ 3.0 4.0) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series151.0ms

Counts
4 → 10
Calls
4 calls:
82.0ms
(* (* (/ 3.0 4.0) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.4s

Counts
188 → 188
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02142724
16512387
232551944
done50011919

prune752.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (+ (* (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow 1.0 3)) (pow (fabs x) 4)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))) (/ 1.0 (fabs x))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) (* (/ 1.0 (sqrt PI)) (exp (pow (fabs x) 2))))
0.4b
(* (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow 1.0 3)) (pow (fabs x) 4)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))) (/ 1.0 (fabs x)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
38×frac-add
35×add-sqr-sqrt
33×*-un-lft-identity
32×associate-*l/
29×add-cube-cbrt
28×times-frac
21×add-cbrt-cube
20×frac-times
19×add-exp-log
14×associate-*r*
13×pow1 unpow-prod-down cube-prod
10×flip3-+ flip-+
8×associate-*l*
7×prod-exp cbrt-unprod
4×associate-*r/ pow-prod-down add-log-exp
3×cbrt-undiv pow-unpow div-exp sqrt-prod div-inv
2×pow-exp *-commutative distribute-lft-out rem-cube-cbrt unswap-sqr
1×cube-div cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 sqr-pow
Counts
4 → 142
Calls
4 calls:
2.5s
(* (+ (+ (* (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow 1.0 3)) (pow (fabs x) 4)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))) (/ 1.0 (fabs x))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) (* (/ 1.0 (sqrt PI)) (exp (pow (fabs x) 2))))
116.0ms
(* (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow 1.0 3)) (pow (fabs x) 4)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series633.0ms

Counts
4 → 10
Calls
4 calls:
429.0ms
(* (+ (+ (* (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow 1.0 3)) (pow (fabs x) 4)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))) (/ 1.0 (fabs x))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) (* (/ 1.0 (sqrt PI)) (exp (pow (fabs x) 2))))
170.0ms
(* (+ (/ (* (* (/ 3.0 4.0) 1.0) (pow 1.0 3)) (pow (fabs x) 4)) (/ (* (/ 15.0 8.0) (pow 1.0 6)) (pow (fabs x) 6))) (/ 1.0 (fabs x)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify504.0ms

Counts
152 → 152
Iterations

Useful iterations: done (496.0ms)

IterNodesCost
03668240
111327881
done50007655

prune841.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes235.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample9.2s

Algorithm
intervals
Results
8.0s103451×body80valid