Details

Time bar (total: 10.9s)

sample32.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms241×body80nan

simplify132.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01114
12114
24113
36913
49413
511813
613113
713313
done13313

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite40.0ms

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))
15.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
17.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

series203.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
78.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
83.0ms
(/ 6.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)))

simplify1.1s

Counts
162 → 162
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02503612
15483468
218733294
done50003288

prune482.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
0.0b
(cbrt (pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3))
0.0b
(/ 6.0 (cbrt (pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3)))
0.0b
(pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3)

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
348×times-frac
264×add-sqr-sqrt *-un-lft-identity
240×cbrt-prod
184×add-cube-cbrt
126×unpow-prod-down cube-prod
56×associate-/r*
40×distribute-lft-out-- difference-of-squares
27×associate-/r/
14×div-inv
13×flip3-- flip--
11×add-exp-log
10×add-cbrt-cube
6×cube-mult unpow3 associate-/l* sqr-pow
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv cube-div pow-unpow div-exp
2×cbrt-div frac-2neg pow-exp clear-num rem-cube-cbrt
1×pow-to-exp pow-pow pow1/3 rem-cbrt-cube
Counts
4 → 385
Calls
4 calls:
16.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
20.0ms
(cbrt (pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3))
59.0ms
(/ 6.0 (cbrt (pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3)))
21.0ms
(pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3)

series520.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0))
121.0ms
(cbrt (pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3))
147.0ms
(/ 6.0 (cbrt (pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3)))
136.0ms
(pow (/ (fma (sqrt x) 4.0 (+ x 1.0)) (- x 1.0)) 3)

simplify1.5s

Counts
397 → 397
Iterations

Useful iterations: done (1.5s)

IterNodesCost
040311165
18209381
224698607
done50008605

prune811.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))
0.3b
(/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0)))
0.3b
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.6b
(* (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))))

rewrite442.0ms

Algorithm
rewrite-expression-head
Rules
1002×times-frac
762×add-sqr-sqrt
614×*-un-lft-identity
563×sqrt-prod
444×add-cube-cbrt
221×associate-*r*
85×distribute-lft-out-- difference-of-squares
47×associate-/r*
40×associate-*l*
35×unswap-sqr
34×add-exp-log add-cbrt-cube
30×associate-/r/
18×div-inv associate-/l*
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
1×frac-times sqrt-undiv associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 717
Calls
4 calls:
18.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))
31.0ms
(/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0)))
9.0ms
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
290.0ms
(* (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))))

series864.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))
237.0ms
(/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0)))
200.0ms
(/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
244.0ms
(* (/ (sqrt 6.0) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (/ (sqrt 6.0) (/ (sqrt (fma (sqrt x) 4.0 (+ x 1.0))) (- x 1.0))))

simplify1.1s

Counts
729 → 729
Iterations

Useful iterations: done (1.1s)

IterNodesCost
068323023
1190620674
done500120236

prune1.8s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes14.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01316
11416
done1416

end0.0ms

sample1.7s

Algorithm
intervals
Results
885.0ms8000×body80valid
419.0ms8200×body80nan