Details

Time bar (total: 14.0s)

sample28.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
7.0ms286×body80nan

simplify82.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01114
12114
24013
36513
48913
511313
612613
712813
done12813

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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)))

rewrite27.0ms

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))
6.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
13.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series204.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
77.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
87.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify870.0ms

Counts
162 → 162
Iterations

Useful iterations: done (864.0ms)

IterNodesCost
02503612
15623468
219093294
done50003292

prune432.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize8.0ms

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)))

rewrite28.0ms

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))
16.0ms
(* 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)))

series213.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
88.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
83.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify1.5s

Counts
99 → 99
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01431667
13541615
29531455
331001453
done50001452

prune251.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

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))))

rewrite216.0ms

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:
62.0ms
(* 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))))))
18.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
94.0ms
(* (/ (+ (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)))))
24.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
504.0ms
(* 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))))))
266.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
411.0ms
(* (/ (+ (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)))))
283.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify1.4s

Counts
307 → 307
Iterations

Useful iterations: done (1.4s)

IterNodesCost
034710059
110259372
233408127
done50008054

prune735.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize24.0ms

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
(* (/ (sqrt 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
(/ (sqrt 1) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
1025×times-frac
844×*-un-lft-identity
774×sqrt-prod
663×add-sqr-sqrt
443×add-cube-cbrt
221×associate-*l*
170×distribute-lft-out
58×associate-*r*
52×difference-of-squares
47×associate-/r*
34×add-exp-log add-cbrt-cube
30×associate-/r/ unswap-sqr
26×distribute-lft-out--
21×associate-/l*
18×div-inv
14×cbrt-undiv flip3-+ div-exp flip-+
6×pow1 prod-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-- div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 753
Calls
4 calls:
13.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
261.0ms
(* (/ (sqrt 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
(/ (sqrt 1) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
536.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0)))
424.0ms
(* (/ (sqrt 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)))))
292.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
282.0ms
(/ (sqrt 1) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (+ (sqrt x) (sqrt 1.0))))

simplify2.3s

Counts
765 → 765
Iterations

Useful iterations: 2 (1.6s)

IterNodesCost
065926650
1191023328
2464820404
done500020404

prune1.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes27.0ms

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

sample633.0ms

Algorithm
intervals
Results
243.0ms8000×body80valid
211.0ms8031×body80nan