Details

Time bar (total: 35.9s)

sample844.0ms

Algorithm
intervals
Results
737.0ms3337×body80valid

simplify3.3s

Counts
1 → 1
Iterations
IterNodes
done5000
31795
2379
190
031

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize119.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
80×times-frac
62×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
20×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×sqrt-prod
4×add-log-exp
2×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 160
Calls
4 calls:
32.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
44.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series80.0ms

Counts
4 → 8
Calls
4 calls:
48.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
31.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.1s

Counts
168 → 168
Iterations
IterNodes
done5000
21626
1449
0143

prune1.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.4b

localize108.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
88×add-sqr-sqrt
80×times-frac
62×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
20×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×sqrt-prod
4×add-log-exp
2×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 160
Calls
4 calls:
28.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series80.0ms

Counts
4 → 8
Calls
4 calls:
45.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
35.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.2s

Counts
168 → 168
Iterations
IterNodes
done5001
21643
1451
0144

prune1.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.3b

localize99.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (/ 1.0 (sqrt PI)) (* (exp (* (fabs x) (fabs x))) (/ 1.0 (fabs x)))) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (/ 1.0 (* (fabs x) (fabs x))) (/ 15.0 8.0)))))))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
506×frac-times
428×associate-*r/
280×frac-add
174×add-cbrt-cube
164×associate-*l/
158×add-exp-log
100×prod-exp cbrt-unprod
48×add-sqr-sqrt
40×flip3-+ times-frac flip-+
38×cbrt-undiv div-exp
34×pow1 *-un-lft-identity add-cube-cbrt
16×pow-prod-down
14×associate-*r* associate-*l*
13×swap-sqr
6×sqrt-prod
4×distribute-rgt-in distribute-lft-in div-inv add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
1×pow2 pow-plus pow-sqr pow-prod-up
Counts
4 → 376
Calls
4 calls:
426.0ms
(* (* (/ 1.0 (sqrt PI)) (* (exp (* (fabs x) (fabs x))) (/ 1.0 (fabs x)))) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (/ 1.0 (* (fabs x) (fabs x))) (/ 15.0 8.0)))))))
33.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series529.0ms

Counts
4 → 8
Calls
4 calls:
502.0ms
(* (* (/ 1.0 (sqrt PI)) (* (exp (* (fabs x) (fabs x))) (/ 1.0 (fabs x)))) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (+ (/ 3.0 4.0) (* (/ 1.0 (* (fabs x) (fabs x))) (/ 15.0 8.0)))))))
26.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify3.6s

Counts
384 → 384
Iterations
IterNodes
done5000
13624
0846

prune3.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize178.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* (* (/ 1.0 (sqrt PI)) (* (exp (* (fabs x) (fabs x))) 1.0)) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* 1.0 (/ 15.0 8.0))))))))) (* (fabs x) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x)))))))
0.4b
(* (/ 1.0 (* (fabs x) (fabs x))) (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* 1.0 (/ 15.0 8.0))))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
1072×add-cbrt-cube
1024×add-exp-log
703×prod-exp cbrt-unprod
236×cbrt-undiv div-exp
15×add-sqr-sqrt
11×frac-times associate-*r/ associate-/l/
10×associate-*l/
9×*-un-lft-identity add-cube-cbrt
8×pow1
7×associate-*l*
6×flip3-+ sqrt-prod flip-+
5×times-frac
4×add-log-exp
3×associate-*r*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv unswap-sqr
1×distribute-rgt-in clear-num associate-/r* frac-2neg distribute-lft-in pow-prod-down *-commutative associate-/l*
Counts
4 → 336
Calls
4 calls:
924.0ms
(/ (* (* (/ 1.0 (sqrt PI)) (* (exp (* (fabs x) (fabs x))) 1.0)) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* 1.0 (/ 15.0 8.0))))))))) (* (fabs x) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x)))))))
589.0ms
(* (/ 1.0 (* (fabs x) (fabs x))) (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* 1.0 (/ 15.0 8.0))))))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series723.0ms

Counts
4 → 8
Calls
4 calls:
520.0ms
(/ (* (* (/ 1.0 (sqrt PI)) (* (exp (* (fabs x) (fabs x))) 1.0)) (* (/ 1.0 (* (fabs x) (fabs x))) (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* 1.0 (/ 15.0 8.0))))))))) (* (fabs x) (* 2.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x)))))))
203.0ms
(* (/ 1.0 (* (fabs x) (fabs x))) (+ (* 1.0 (* (fabs x) (* 4.0 (* (fabs x) (fabs x))))) (* 2.0 (* (* 1.0 (/ 1.0 (fabs x))) (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* 1.0 (/ 15.0 8.0))))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify4.7s

Counts
344 → 344
Iterations
IterNodes
done5011
11954
0541

prune3.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes735.0ms

bsearch0.0ms

simplify39.0ms

Iterations
IterNodes
done62
162
041

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.6s13294×body80valid