Details

Time bar (total: 12.4s)

sample38.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
10.0ms275×body80nan

simplify152.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
01114
12114
24113
37013
49913
512813
614113
714313
done14313

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite48.0ms

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))
12.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
24.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series230.0ms

Counts
3 → 9
Calls
3 calls:
43.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
91.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
95.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.8s

Counts
162 → 162
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02503612
16313490
230383298
done50013288

prune535.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

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 4.0 (sqrt x) (+ x 1.0))
26.0ms
(* 6.0 (/ (- x 1.0) (fma 4.0 (sqrt x) (+ x 1.0))))
31.0ms
(/ (- x 1.0) (fma 4.0 (sqrt x) (+ x 1.0)))

series250.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(fma 4.0 (sqrt x) (+ x 1.0))
109.0ms
(* 6.0 (/ (- x 1.0) (fma 4.0 (sqrt x) (+ x 1.0))))
91.0ms
(/ (- x 1.0) (fma 4.0 (sqrt x) (+ x 1.0)))

simplify1.1s

Counts
99 → 99
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01431667
13731623
215361463
done50011459

prune257.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
205×add-sqr-sqrt
197×*-un-lft-identity
195×sqrt-prod
170×times-frac
93×add-cube-cbrt
92×associate-*r*
52×difference-of-squares
34×add-exp-log add-cbrt-cube
26×distribute-lft-out distribute-lft-out--
14×associate-/l*
12×prod-exp associate-/r* cbrt-unprod
11×pow1
8×cbrt-undiv div-exp
4×expm1-log1p-u associate-*r/ associate-*l* pow-prod-down log1p-expm1-u div-inv associate-/l/ add-log-exp
3×unswap-sqr
2×frac-2neg clear-num *-commutative
1×frac-times flip3-- flip3-+ div-sub associate-*l/ flip-- flip-+
Counts
4 → 285
Calls
4 calls:
122.0ms
(* (* 6.0 (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
65.0ms
(* 6.0 (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
64.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))
51.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
525.0ms
(* (* 6.0 (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
317.0ms
(* 6.0 (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
298.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))
271.0ms
(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))

simplify643.0ms

Counts
297 → 297
Iterations

Useful iterations: done (630.0ms)

IterNodesCost
03448749
110608025
done50007415

prune855.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (sqrt 1.0) (sqrt x)))
0.1b
(* (* 6.0 (sqrt (+ (sqrt 1.0) (sqrt x)))) (/ (sqrt (+ (sqrt x) (sqrt 1.0))) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
0.2b
(* 6.0 (sqrt (+ (sqrt 1.0) (sqrt x))))
0.2b
(/ (sqrt (+ (sqrt x) (sqrt 1.0))) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
161×sqrt-prod
129×*-un-lft-identity
96×times-frac
82×add-sqr-sqrt
69×add-cube-cbrt
60×associate-*r*
30×distribute-lft-out
20×add-exp-log add-cbrt-cube
12×pow1
10×sqrt-div
8×associate-/l*
7×associate-*r/ prod-exp cbrt-unprod
6×associate-/r*
5×flip3-+ flip-+
4×expm1-log1p-u associate-*l* pow-prod-down hypot-def log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp
2×frac-times associate-*l/ *-commutative div-inv associate-/l/ unswap-sqr
1×rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 208
Calls
4 calls:
19.0ms
(sqrt (+ (sqrt 1.0) (sqrt x)))
106.0ms
(* (* 6.0 (sqrt (+ (sqrt 1.0) (sqrt x)))) (/ (sqrt (+ (sqrt x) (sqrt 1.0))) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
39.0ms
(* 6.0 (sqrt (+ (sqrt 1.0) (sqrt x))))
29.0ms
(/ (sqrt (+ (sqrt x) (sqrt 1.0))) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
128.0ms
(sqrt (+ (sqrt 1.0) (sqrt x)))
330.0ms
(* (* 6.0 (sqrt (+ (sqrt 1.0) (sqrt x)))) (/ (sqrt (+ (sqrt x) (sqrt 1.0))) (sqrt (fma 4.0 (sqrt x) (+ x 1.0)))))
226.0ms
(* 6.0 (sqrt (+ (sqrt 1.0) (sqrt x))))
370.0ms
(/ (sqrt (+ (sqrt x) (sqrt 1.0))) (sqrt (fma 4.0 (sqrt x) (+ x 1.0))))

simplify556.0ms

Counts
220 → 220
Iterations

Useful iterations: done (547.0ms)

IterNodesCost
03735691
110344852
done50004519

prune785.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11213
done1213

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s8000×body80valid
374.0ms8189×body80nan