Details

Time bar (total: 40.2s)

sample79.0ms

Algorithm
intervals
Results
59.0ms422×body80valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite16.6s

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×add-cube-cbrt *-un-lft-identity
15×associate-*l/
13×sqrt-prod
12×frac-add
11×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 173
Calls
4 calls:
14.4s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
2.1s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
92.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series646.0ms

Counts
4 → 10
Calls
4 calls:
92.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
495.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
58.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify960.0ms

Counts
183 → 183
Iterations

Useful iterations: done (950.0ms)

IterNodesCost
03849064
112306340
done50004892

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt PI) (cbrt PI))
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
12.0ms
(* (cbrt PI) (cbrt PI))
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(* (cbrt PI) (cbrt PI))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify1.7s

Counts
85 → 85
Iterations

Useful iterations: done (1.7s)

IterNodesCost
078720
1151635
2409601
31242569
done5000549

prune841.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 3.0 (pow (fabs x) 3))
0.3b
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
1.0b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
438×times-frac
235×add-sqr-sqrt
234×add-cube-cbrt *-un-lft-identity
74×associate-/r*
48×unpow-prod-down cube-prod
39×sqrt-prod
24×add-exp-log
16×cube-mult unpow3 add-cbrt-cube sqr-pow
13×div-exp
11×div-inv
9×associate-/l*
7×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-to-exp pow-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 372
Calls
4 calls:
19.0ms
(/ 3.0 (pow (fabs x) 3))
24.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
50.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
3.0ms
(sqrt PI)

series575.0ms

Counts
4 → 10
Calls
4 calls:
71.0ms
(/ 3.0 (pow (fabs x) 3))
428.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
75.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify2.8s

Counts
382 → 382
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
054410863
110739979
237939589
done50009589

prune2.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) 1.0))
1.0b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
297×times-frac
153×add-sqr-sqrt
151×add-cube-cbrt *-un-lft-identity
47×associate-/r*
36×unpow-prod-down cube-prod
23×add-exp-log
18×add-cbrt-cube
12×cube-mult unpow3 div-exp sqr-pow
10×div-inv
8×cbrt-undiv
6×pow1 sqrt-prod associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/r/
1×pow-to-exp pow-exp prod-exp cbrt-unprod
Counts
4 → 262
Calls
4 calls:
18.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) 1.0))
20.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
3.0ms
(sqrt PI)
4.0ms
(sqrt PI)

series468.0ms

Counts
4 → 8
Calls
4 calls:
412.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) 1.0))
56.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.7s

Counts
270 → 270
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
04536624
18915732
232695334
done50015334

prune1.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes113.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02739
done2739

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.2s14061×body80valid