Details

Time bar (total: 16.0s)

sample40.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
11.0ms288×body80nan

simplify140.0ms

Counts
1 → 1
Iterations
IterNodes
done143
7143
6141
5128
499
370
241
121
011

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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)))

rewrite51.0ms

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-cbrt-cube add-exp-log
7×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l*
3×expm1-log1p-u associate-/r* associate-*l* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr associate-/l/
1×clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative fma-udef flip--
Counts
3 → 90
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
31.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
14.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series257.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(fma (sqrt x) 4.0 (+ x 1.0))
115.0ms
(* 6.0 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))
93.0ms
(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify956.0ms

Counts
99 → 99
Iterations
IterNodes
done5001
21541
1374
0144

prune559.0ms

Pruning

5 alts after pruning (5 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)
0.0b
(/ (+ (fma (sqrt x) 4.0 x) 1.0) (- x 1.0))
0.1b
(/ 6.0 (/ (+ (fma (sqrt x) 4.0 x) 1.0) (- x 1.0)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
175×*-un-lft-identity
123×add-sqr-sqrt
81×add-cube-cbrt
31×associate-/r*
26×distribute-lft-out
21×distribute-lft-out-- difference-of-squares
11×associate-/r/
10×add-cbrt-cube add-exp-log
7×associate-/l*
6×div-inv
5×flip3-- flip--
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
2×clear-num frac-2neg associate-/l/
1×flip3-+ flip-+ fma-udef
Counts
3 → 181
Calls
3 calls:
0.0ms
(fma (sqrt x) 4.0 x)
36.0ms
(/ (+ (fma (sqrt x) 4.0 x) 1.0) (- x 1.0))
23.0ms
(/ 6.0 (/ (+ (fma (sqrt x) 4.0 x) 1.0) (- x 1.0)))

series274.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(fma (sqrt x) 4.0 x)
118.0ms
(/ (+ (fma (sqrt x) 4.0 x) 1.0) (- x 1.0))
105.0ms
(/ 6.0 (/ (+ (fma (sqrt x) 4.0 x) 1.0) (- x 1.0)))

simplify1.5s

Counts
190 → 190
Iterations
IterNodes
done5000
23446
1699
0267

prune890.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 6.0 (log1p (expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0)))))
0.1b
(log1p (expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0))))
0.1b
(/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0))
0.4b
(expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
29×add-sqr-sqrt
20×times-frac
17×add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×pow1 distribute-lft-out
5×log1p-expm1-u associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u associate-/r* add-log-exp
3×associate-*r* associate-*l*
2×associate-/r/ associate-/l/
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg flip3-+ flip3-- div-sub div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-+ div-inv flip-- expm1-udef unswap-sqr
Counts
4 → 90
Calls
4 calls:
5.0ms
(* 6.0 (log1p (expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0)))))
0.0ms
(log1p (expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0))))
19.0ms
(/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0))
0.0ms
(expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0)))

series800.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(* 6.0 (log1p (expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0)))))
297.0ms
(log1p (expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0))))
104.0ms
(/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0))
154.0ms
(expm1 (/ (- x 1.0) (+ (fma (sqrt x) 4.0 x) 1.0)))

simplify937.0ms

Counts
102 → 102
Iterations
IterNodes
done5000
21500
1401
0163

prune607.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))
0.1b
(log1p (expm1 (* (/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))))))
0.1b
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))
0.4b
(expm1 (* (/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
148×*-un-lft-identity
128×sqrt-prod
116×add-sqr-sqrt
98×times-frac
52×add-cube-cbrt
32×distribute-lft-out difference-of-squares
16×distribute-lft-out--
14×associate-/r* associate-/l*
8×add-cbrt-cube add-exp-log
5×log1p-expm1-u
4×expm1-log1p-u pow1 sqrt-div associate-/r/ add-log-exp associate-/l/
3×flip3-+ flip-+
2×cbrt-undiv clear-num frac-2neg div-exp div-inv
1×log1p-udef expm1-log1p flip3-- div-sub log1p-expm1 flip-- expm1-udef
Counts
4 → 185
Calls
4 calls:
51.0ms
(/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))
0.0ms
(log1p (expm1 (* (/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))))))
52.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))
0.0ms
(expm1 (* (/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))))

series4.3s

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))
2.0s
(log1p (expm1 (* (/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))))))
361.0ms
(/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))
1.6s
(expm1 (* (/ (+ (sqrt 1.0) (sqrt x)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0))) (/ (- (sqrt x) (sqrt 1.0)) (sqrt (+ (fma (sqrt x) 4.0 x) 1.0)))))

simplify1.8s

Counts
197 → 197
Iterations
IterNodes
done5000
24323
1972
0366

prune1.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
217
116
012

end0.0ms

sample1.5s

Algorithm
intervals
Results
659.0ms8000×body80valid
508.0ms7906×body80nan