Details

Time bar (total: 8.3s)

sample312.0ms

Algorithm
intervals
Results
256.0ms3391×body80valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
09061
138958
2211536
3500136

prune14.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.4b

Counts
2 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
216×frac-add
180×associate-*l/
153×frac-times
94×times-frac
83×associate-/l/
63×associate-*r/
62×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
42×cube-div
26×unpow-prod-down cube-prod
22×associate-/r* add-cbrt-cube
21×sqrt-prod
20×add-exp-log
10×flip3-+ flip-+
8×cbrt-undiv div-exp
7×pow1 div-inv
6×pow-unpow
4×pow-exp add-log-exp rem-cube-cbrt
2×cube-mult pow-to-exp pow-pow unpow3 prod-exp cbrt-unprod sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/ associate-/l*
Counts
4 → 252
Calls
4 calls:
110.0ms
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series519.0ms

Counts
4 → 10
Calls
4 calls:
446.0ms
(/ (* (+ (+ (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (pow (/ 1.0 (fabs x)) 3)) (+ (/ 3.0 4.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 15.0 8.0)))) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
39.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify82.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
016635570
150014966

prune1.4s

Filtered
262 candidates to 184 candidates (70.2%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New24616262
Fresh101
Picked101
Done000
Total24816264

Merged error: 0.0b

Counts
264 → 16

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 5))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 5)))
0.3b
(/ 1 (pow (fabs x) 7))
0.4b
(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
146×associate-*r/
136×frac-add
85×un-div-inv
78×times-frac
74×add-sqr-sqrt
62×*-un-lft-identity
59×add-cube-cbrt
46×add-exp-log
41×associate-*r*
35×unpow-prod-down
31×sqrt-div
30×frac-times associate-*l/
18×div-exp add-cbrt-cube
14×flip3-+ associate-/r* flip-+
13×prod-exp sqrt-prod sqr-pow
11×pow1
9×pow-to-exp rec-exp 1-exp pow-exp
7×unswap-sqr
6×associate-/l*
5×cbrt-unprod
4×associate-*l* pow-prod-down div-inv add-log-exp
3×cbrt-undiv
2×pow-flip frac-2neg clear-num *-commutative inv-pow
Counts
4 → 256
Calls
4 calls:
5.0ms
(/ 1 (pow (fabs x) 5))
11.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
8.0ms
(/ 1 (pow (fabs x) 7))
35.0ms
(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

series577.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 1 (pow (fabs x) 5))
56.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
68.0ms
(/ 1 (pow (fabs x) 7))
402.0ms
(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (/ 1 (pow (fabs x) 7))))))) (sqrt (/ 1 PI)))

simplify79.0ms

Algorithm
egg-herbie
Counts
268 → 268
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015865281
150014895

prune999.0ms

Filtered
268 candidates to 131 candidates (48.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2644268
Fresh10515
Picked101
Done000
Total2759284

Merged error: 0.0b

Counts
284 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1.875 (pow (fabs x) (- 7)))
0.3b
(/ 1 (pow (fabs x) 5))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 5)))
0.4b
(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (pow (fabs x) (- 7))))))) (sqrt (/ 1 PI)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
204×associate-*r/
184×frac-add
110×un-div-inv
66×add-sqr-sqrt
57×times-frac
49×*-un-lft-identity
48×associate-*r*
46×add-cube-cbrt
42×add-exp-log
39×sqrt-div
38×frac-times associate-*l/
34×pow-neg
27×unpow-prod-down
18×add-cbrt-cube
17×neg-sub0 pow-sub
16×prod-exp
14×flip3-+ flip-+
13×sqrt-prod
12×div-exp
11×pow1 sqr-pow
10×unswap-sqr
7×pow-to-exp associate-*l* pow-exp associate-/r*
6×rec-exp 1-exp cbrt-unprod
4×pow-prod-down add-log-exp
3×*-commutative div-inv associate-/l*
2×cbrt-undiv
1×pow-flip frac-2neg clear-num inv-pow
Counts
4 → 247
Calls
4 calls:
5.0ms
(* 1.875 (pow (fabs x) (- 7)))
5.0ms
(/ 1 (pow (fabs x) 5))
10.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
37.0ms
(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (pow (fabs x) (- 7))))))) (sqrt (/ 1 PI)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* 1.875 (pow (fabs x) (- 7)))
51.0ms
(/ 1 (pow (fabs x) 5))
57.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))
403.0ms
(* (* (exp (pow (fabs x) 2)) (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (+ (* 0.75 (/ 1 (pow (fabs x) 5))) (+ (* 1.0 (/ 1 (fabs x))) (* 1.875 (pow (fabs x) (- 7))))))) (sqrt (/ 1 PI)))

simplify77.0ms

Algorithm
egg-herbie
Counts
259 → 259
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
017475764
150015384

prune1.1s

Filtered
259 candidates to 122 candidates (47.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2590259
Fresh088
Picked011
Done000
Total2599268

Merged error: 0.0b

Counts
268 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.5 (pow (fabs x) 3))
0.3b
(/ 1.875 (pow (fabs x) 7))
0.3b
(/ 0.75 (pow (fabs x) 5))
0.4b
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
93×times-frac
88×*-un-lft-identity
79×add-sqr-sqrt
70×add-cube-cbrt
36×unpow-prod-down
26×associate-/r*
21×add-exp-log
18×frac-add
16×associate-*l* sqrt-prod
12×cube-prod add-cbrt-cube sqr-pow
9×div-exp distribute-lft-out associate-/l*
8×sqrt-div
7×frac-times associate-*r/ associate-*r*
6×pow1 flip3-+ flip-+
4×cube-mult unpow3 div-inv add-log-exp unswap-sqr
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 210
Calls
4 calls:
5.0ms
(/ 0.5 (pow (fabs x) 3))
5.0ms
(/ 1.875 (pow (fabs x) 7))
5.0ms
(/ 0.75 (pow (fabs x) 5))
53.0ms
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))))

series493.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 0.5 (pow (fabs x) 3))
69.0ms
(/ 1.875 (pow (fabs x) 7))
52.0ms
(/ 0.75 (pow (fabs x) 5))
331.0ms
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ 1.875 (pow (fabs x) 7)) (/ 1.0 (fabs x))) (/ 0.75 (pow (fabs x) 5))) (/ 0.5 (pow (fabs x) 3))))

simplify50.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010302582
150022479

prune939.0ms

Filtered
222 candidates to 145 candidates (65.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2220222
Fresh077
Picked011
Done011
Total2229231

Merged error: 0.0b

Counts
231 → 9

regimes160.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample332.0ms

Algorithm
intervals
Results
278.0ms3685×body80valid