Details

Time bar (total: 12.4s)

sample28.0ms

Algorithm
intervals
Results
8.0ms286×body80nan
8.0ms256×body80valid

simplify109.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
12114
24013
36513
48913
511313
612613
712813
done12813

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
0.0b
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
103×add-sqr-sqrt *-un-lft-identity
71×add-cube-cbrt
26×associate-/r*
16×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-exp-log add-cbrt-cube
6×div-inv associate-/l*
5×flip3-- flip--
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×fma-udef
Counts
3 → 153
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
5.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
9.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series193.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
73.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
81.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify797.0ms

Counts
162 → 162
Iterations

Useful iterations: done (791.0ms)

IterNodesCost
02503612
15623468
219113294
done50003292

prune433.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (sqrt x) 4.0 (+ x 1.0))
0.0b
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
0.1b
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
37×*-un-lft-identity
31×times-frac
23×add-cube-cbrt
19×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l*
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num *-commutative flip-- fma-udef
Counts
3 → 90
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
15.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
9.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series191.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
80.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
74.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify1.7s

Counts
99 → 99
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01431667
13541615
29551455
331061453
done50011452

prune249.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 6.0 (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
0.0b
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.0b
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
0.0b
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
227×add-sqr-sqrt
200×sqrt-prod
197×*-un-lft-identity
180×times-frac
93×add-cube-cbrt
59×associate-*r*
52×difference-of-squares
38×add-exp-log add-cbrt-cube
37×associate-*l*
26×distribute-lft-out distribute-lft-out--
14×associate-/l*
13×prod-exp cbrt-unprod
12×associate-/r*
11×pow1
10×cbrt-undiv div-exp
9×unswap-sqr
5×associate-*r/
4×expm1-log1p-u pow-prod-down log1p-expm1-u div-inv associate-/l/ add-log-exp
2×frac-times frac-2neg associate-*l/ clear-num *-commutative
1×flip3-- flip3-+ div-sub flip-- flip-+
Counts
4 → 295
Calls
4 calls:
57.0ms
(* 6.0 (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
21.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
88.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
23.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
454.0ms
(* 6.0 (* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))))
250.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
374.0ms
(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
257.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify1.5s

Counts
307 → 307
Iterations

Useful iterations: done (1.5s)

IterNodesCost
034710059
110259426
234298135
done50018082

prune693.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
0.0b
(* (/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
0.0b
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.1b
(/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

rewrite268.0ms

Algorithm
rewrite-expression-head
Rules
608×times-frac
525×*-un-lft-identity
449×add-sqr-sqrt
369×sqrt-prod
268×add-cube-cbrt
113×associate-*l*
98×distribute-lft-out
64×add-exp-log
58×associate-*r*
52×difference-of-squares
47×associate-/r*
34×add-cbrt-cube
30×div-exp
26×distribute-lft-out--
21×unswap-sqr
18×associate-/r/ associate-/l*
14×cbrt-undiv prod-exp
12×div-inv
8×flip3-+ flip-+
7×pow1
6×rec-exp 1-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×frac-times flip3-- pow-flip div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 539
Calls
4 calls:
13.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
165.0ms
(* (/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
23.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
23.0ms
(/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
465.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
396.0ms
(* (/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))))
272.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
251.0ms
(/ 1 (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

simplify1.3s

Counts
551 → 551
Iterations

Useful iterations: done (1.3s)

IterNodesCost
057818033
1169416411
done500214607

prune1.1s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11213
done1213

end0.0ms

sample695.0ms

Algorithm
intervals
Results
263.0ms8000×body80valid
231.0ms8031×body80nan