Details

Time bar (total: 19.6s)

sample344.0ms

Algorithm
intervals
Results
282.0ms3513×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (189.0ms)

IterNodesCost
031103
190103
238165
3195451
done500151

prune16.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 222
Calls
4 calls:
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
16.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms
(sqrt PI)

series77.0ms

Counts
4 → 10
Calls
4 calls:
24.0ms
(* (/ 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)

simplify704.0ms

Counts
232 → 232
Iterations

Useful iterations: done (697.0ms)

IterNodesCost
01503287
14242964
216132446
done50002437

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.4b

localize31.0ms

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)

rewrite23.0ms

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 expm1-log1p-u log1p-expm1-u 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 → 163
Calls
4 calls:
9.0ms
(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)

series125.0ms

Counts
4 → 10
Calls
4 calls:
58.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify894.0ms

Counts
173 → 173
Iterations

Useful iterations: 2 (354.0ms)

IterNodesCost
01932107
15571874
220931513
done50001513

prune695.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
67×frac-times
55×associate-*r/
49×add-sqr-sqrt
46×times-frac
45×associate-*l/
43×add-cube-cbrt *-un-lft-identity
42×frac-add
26×cube-div unpow-prod-down cube-prod
15×add-exp-log add-cbrt-cube
13×associate-*l*
9×pow1
6×pow-unpow
5×div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×cbrt-undiv div-exp associate-*r* sqrt-prod
2×cube-mult pow-to-exp pow-pow flip3-+ unpow3 prod-exp cbrt-unprod flip-+ unswap-sqr sqr-pow
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 193
Calls
4 calls:
130.0ms
(* (/ 1.0 (fabs x)) (+ (* (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 3)) (/ 1.0 (fabs x))) (* (/ 15.0 8.0) (/ (pow 1.0 6) (pow (fabs x) 6)))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series237.0ms

Counts
4 → 10
Calls
4 calls:
170.0ms
(* (/ 1.0 (fabs x)) (+ (* (* (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 3)) (/ 1.0 (fabs x))) (* (/ 15.0 8.0) (/ (pow 1.0 6) (pow (fabs x) 6)))))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify502.0ms

Counts
203 → 203
Iterations

Useful iterations: done (495.0ms)

IterNodesCost
03624823
114154494
done50014471

prune1.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
19×add-cbrt-cube
18×add-exp-log
9×sqrt-prod
7×pow1
6×pow-unpow associate-/r*
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×prod-exp cbrt-unprod
2×cube-div cube-mult pow-to-exp pow-pow unpow3 associate-*r/ associate-/l/ sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 clear-num flip-+ associate-/l*
Counts
4 → 144
Calls
4 calls:
59.0ms
(/ (* (* 1.0 (exp (pow (fabs x) 2))) (+ (/ (* 1.0 (fma (* (* 3.0 (pow (/ 1.0 (fabs x)) 3)) (/ 1.0 (fabs x))) (pow (fabs x) 6) (* 4.0 (* (/ 15.0 8.0) (pow 1.0 6))))) (* (* 4.0 (fabs x)) (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 3) (/ 1.0 2.0) (/ 1.0 (fabs x))))) (sqrt PI))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series628.0ms

Counts
4 → 10
Calls
4 calls:
556.0ms
(/ (* (* 1.0 (exp (pow (fabs x) 2))) (+ (/ (* 1.0 (fma (* (* 3.0 (pow (/ 1.0 (fabs x)) 3)) (/ 1.0 (fabs x))) (pow (fabs x) 6) (* 4.0 (* (/ 15.0 8.0) (pow 1.0 6))))) (* (* 4.0 (fabs x)) (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 3) (/ 1.0 2.0) (/ 1.0 (fabs x))))) (sqrt PI))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.0s

Counts
154 → 154
Iterations

Useful iterations: 2 (446.0ms)

IterNodesCost
02094268
16214079
226353184
done50013184

prune694.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes282.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample9.6s

Algorithm
intervals
Results
8.2s103451×body80valid