Details

Time bar (total: 25.1s)

sample344.0ms

Algorithm
intervals
Results
283.0ms3558×body80valid

simplify958.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (187.0ms)

IterNodesCost
031103
190103
238165
3195451
done500151

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize35.0ms

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)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms
(sqrt PI)

series71.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
24.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify907.0ms

Counts
232 → 232
Iterations

Useful iterations: done (896.0ms)

IterNodesCost
01503287
14242964
216392446
done50002437

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(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)

rewrite24.0ms

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:
10.0ms
(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)

series128.0ms

Counts
4 → 10
Calls
4 calls:
60.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.1s

Counts
173 → 173
Iterations

Useful iterations: 2 (387.0ms)

IterNodesCost
01932107
15611869
221021505
done50001505

prune733.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (exp (pow (fabs x) 2)) (/ 1.0 (sqrt PI))) (+ (* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x)))) (* (/ 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)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
26×unpow-prod-down cube-prod
19×add-cbrt-cube
17×add-exp-log
12×pow1
6×pow-unpow
5×associate-*r/ prod-exp cbrt-unprod
4×expm1-log1p-u pow-exp log1p-expm1-u div-inv add-log-exp rem-cube-cbrt
3×cbrt-undiv div-exp associate-*r* pow-prod-down sqrt-prod
2×cube-div cube-mult frac-times pow-to-exp pow-pow flip3-+ unpow3 flip-+ sqr-pow
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*l* associate-*l/ *-commutative
Counts
4 → 140
Calls
4 calls:
183.0ms
(* (* (exp (pow (fabs x) 2)) (/ 1.0 (sqrt PI))) (+ (* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x)))) (* (/ 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)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series686.0ms

Counts
4 → 10
Calls
4 calls:
615.0ms
(* (* (exp (pow (fabs x) 2)) (/ 1.0 (sqrt PI))) (+ (* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x)))) (* (/ 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)) 3)
0.0ms
(sqrt PI)

simplify1.2s

Counts
150 → 150
Iterations

Useful iterations: 2 (456.0ms)

IterNodesCost
02083828
16613370
229282790
done50002790

prune700.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.9s

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity times-frac
63×add-sqr-sqrt
54×add-cube-cbrt
36×frac-add
26×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
19×associate-/r*
18×pow1
17×associate-*r/ associate-*r*
16×sqrt-div sqrt-prod
14×frac-times associate-*l/
12×flip3-+ cube-prod flip-+
9×pow-prod-down prod-exp cbrt-unprod distribute-lft-out
8×associate-*l* sqr-pow
6×div-exp associate-/l*
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num *-commutative
Counts
4 → 208
Calls
4 calls:
4.0ms
(/ 0.5 (pow (fabs x) 3))
4.0ms
(/ 1.875 (pow (fabs x) 7))
1.6s
(* (+ (+ (/ 1.875 (pow (fabs x) 7)) (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5)))) (/ 0.5 (pow (fabs x) 3))) (sqrt (/ 1 PI)))
1.2s
(* (* (exp (pow (fabs x) 2)) 1.0) (* (+ (+ (/ 1.875 (pow (fabs x) 7)) (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5)))) (/ 0.5 (pow (fabs x) 3))) (sqrt (/ 1 PI))))

series877.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 0.5 (pow (fabs x) 3))
69.0ms
(/ 1.875 (pow (fabs x) 7))
329.0ms
(* (+ (+ (/ 1.875 (pow (fabs x) 7)) (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5)))) (/ 0.5 (pow (fabs x) 3))) (sqrt (/ 1 PI)))
442.0ms
(* (* (exp (pow (fabs x) 2)) 1.0) (* (+ (+ (/ 1.875 (pow (fabs x) 7)) (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5)))) (/ 0.5 (pow (fabs x) 3))) (sqrt (/ 1 PI))))

simplify1.8s

Counts
220 → 220
Iterations

Useful iterations: done (1.8s)

IterNodesCost
04036893
110366365
241995728
done50005721

prune979.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes184.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample10.0s

Algorithm
intervals
Results
8.6s109911×body80valid