Details

Time bar (total: 11.9s)

sample314.0ms

Algorithm
intervals
Results
257.0ms3276×body80valid

simplify670.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (144.0ms)

IterNodesCost
031103
190103
238365
3198351
done500151

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log cube-prod
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 123
Calls
4 calls:
4.0ms
(pow (/ 1.0 (fabs x)) 3)
3.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
7.0ms
(pow (/ 1.0 (fabs x)) 6)

series117.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(pow (/ 1.0 (fabs x)) 3)
37.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
48.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify907.0ms

Counts
133 → 133
Iterations

Useful iterations: done (903.0ms)

IterNodesCost
02071440
15391318
218731186
done50011181

prune604.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (/ 1.0 (fabs x)) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0)) (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
26×unpow-prod-down
13×cube-prod
10×add-exp-log
7×pow1 add-cbrt-cube
6×pow-unpow
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
2×pow-to-exp pow-pow div-exp rem-cube-cbrt sqr-pow
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 fma-udef
Counts
4 → 103
Calls
4 calls:
0.0ms
(fma (/ 1.0 (fabs x)) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0)) (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
3.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series278.0ms

Counts
4 → 10
Calls
4 calls:
207.0ms
(fma (/ 1.0 (fabs x)) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0)) (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x))))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
37.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify900.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
01871631
14871526
219071334
done50001334

prune548.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
61×times-frac
48×add-sqr-sqrt
47×add-cube-cbrt
30×frac-add
24×unpow-prod-down
23×associate-*l/
21×add-exp-log
19×associate-/r*
17×add-cbrt-cube
14×flip3-+ flip-+
12×cube-prod
11×frac-times distribute-lft-out
10×pow1
8×associate-*l* sqr-pow
7×div-exp
6×associate-/l*
5×prod-exp cbrt-unprod
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-prod-down sqrt-prod
2×pow-to-exp frac-2neg pow-exp clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*r* *-commutative
Counts
4 → 179
Calls
4 calls:
4.0ms
(/ 0.5 (pow (fabs x) 3))
4.0ms
(/ 0.75 (pow (fabs x) 5))
1.1s
(* (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))))
1.0ms
(sqrt PI)

series531.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(/ 0.5 (pow (fabs x) 3))
57.0ms
(/ 0.75 (pow (fabs x) 5))
437.0ms
(* (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))))
0.0ms
(sqrt PI)

simplify403.0ms

Counts
189 → 189
Iterations

Useful iterations: done (396.0ms)

IterNodesCost
03705301
110394791
done50014409

prune893.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.875 (pow (fabs x) 7))
0.2b
(/ 0.5 (pow (fabs x) 3))
0.2b
(* (* (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (* (exp (pow (fabs x) 2)) 1.0)) (sqrt (/ 1 PI)))
0.3b
(/ 0.75 (pow (fabs x) 5))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
87×times-frac
69×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
33×associate-*l/
30×frac-add
27×add-exp-log
26×associate-/r*
19×add-cbrt-cube
16×associate-*r*
14×flip3-+ flip-+
13×pow1 sqrt-prod
12×sqrt-div cube-prod sqr-pow
11×frac-times
9×div-exp associate-/l*
6×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×associate-*r/ associate-*l* *-commutative
Counts
4 → 220
Calls
4 calls:
3.0ms
(/ 1.875 (pow (fabs x) 7))
4.0ms
(/ 0.5 (pow (fabs x) 3))
1.2s
(* (* (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (* (exp (pow (fabs x) 2)) 1.0)) (sqrt (/ 1 PI)))
4.0ms
(/ 0.75 (pow (fabs x) 5))

series601.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 1.875 (pow (fabs x) 7))
41.0ms
(/ 0.5 (pow (fabs x) 3))
439.0ms
(* (* (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (* (exp (pow (fabs x) 2)) 1.0)) (sqrt (/ 1 PI)))
56.0ms
(/ 0.75 (pow (fabs x) 5))

simplify447.0ms

Counts
232 → 232
Iterations

Useful iterations: done (434.0ms)

IterNodesCost
04776231
112575673
done50005474

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes207.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample985.0ms

Algorithm
intervals
Results
841.0ms10836×body80valid