Details

Time bar (total: 35.0s)

sample39.0ms

Algorithm
intervals
Results
14.0ms58×body1280valid
7.0ms37×body640valid
7.0ms126×body80valid
4.0ms25×body320valid
1.0ms10×body160valid

simplify145.0ms

Counts
1 → 1
Iterations
IterNodes
17206
16206
15204
14192
13143
12112
1199
1090
968
851
740
630
524
421
320
217
113
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))
3.1b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
1284×*-un-lft-identity
984×times-frac
841×add-sqr-sqrt
612×prod-diff
521×add-cube-cbrt
251×distribute-lft-out
158×difference-of-squares
110×associate-/r/
90×distribute-lft-out--
77×difference-of-sqr-1
55×div-inv
37×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 753
Calls
3 calls:
29.0ms
(/ (+ x 1) (- x 1))
11.0ms
(/ x (+ x 1))
68.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series163.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(/ (+ x 1) (- x 1))
24.0ms
(/ x (+ x 1))
112.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.5s

Counts
762 → 762
Iterations
IterNodes
23098
11349
0584

prune7.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (* x x))
0.2b
(/ 1 (* x x))
0.6b
(/ -3 (* x (* x x)))
5.0b
(- (/ -3 (* x (* x x))) (+ (/ 1 (* x x)) (/ 3 x)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
42×prod-diff
36×times-frac
33×add-sqr-sqrt
30×add-cube-cbrt
29×add-exp-log
26×pow1
25×div-inv
23×add-cbrt-cube
16×distribute-lft-out
9×prod-exp add-log-exp
8×distribute-rgt-out
7×fma-neg div-exp cbrt-unprod
6×pow-prod-up pow-flip associate-/l*
5×cbrt-undiv
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u distribute-lft-out--
3×associate-*l* frac-sub
2×pow2 rec-exp clear-num associate-/r* frac-2neg pow-plus diff-log 1-exp pow-sqr
1×sum-log sub-neg flip3-+ flip3-- cube-unmult associate-*r* frac-add *-commutative flip-+ flip-- associate--r+ inv-pow difference-of-squares unswap-sqr
Counts
4 → 162
Calls
4 calls:
15.0ms
(* x (* x x))
12.0ms
(/ 1 (* x x))
18.0ms
(/ -3 (* x (* x x)))
123.0ms
(- (/ -3 (* x (* x x))) (+ (/ 1 (* x x)) (/ 3 x)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* x (* x x))
20.0ms
(/ 1 (* x x))
51.0ms
(/ -3 (* x (* x x)))
31.0ms
(- (/ -3 (* x (* x x))) (+ (/ 1 (* x x)) (/ 3 x)))

simplify13.3s

Counts
174 → 174
Iterations
IterNodes
37656
21906
1581
0224

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ x (+ x 1)))
0.4b
(cbrt (/ x (+ x 1)))
6.7b
(fma (* (cbrt (/ x (+ x 1))) (cbrt (/ x (+ x 1)))) (cbrt (/ x (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
34.0b
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
32×*-un-lft-identity
24×times-frac
20×add-sqr-sqrt add-cube-cbrt
6×distribute-lft-out
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-div flip3-+ pow1/3 flip-+ fma-udef div-inv
Counts
4 → 82
Calls
4 calls:
4.0ms
(cbrt (/ x (+ x 1)))
3.0ms
(cbrt (/ x (+ x 1)))
0.0ms
(fma (* (cbrt (/ x (+ x 1))) (cbrt (/ x (+ x 1)))) (cbrt (/ x (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

series665.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(cbrt (/ x (+ x 1)))
88.0ms
(cbrt (/ x (+ x 1)))
359.0ms
(fma (* (cbrt (/ x (+ x 1))) (cbrt (/ x (+ x 1)))) (cbrt (/ x (+ x 1))) (- (* (/ 1 (- x 1)) (+ x 1))))
135.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

simplify1.3s

Counts
94 → 94
Iterations
IterNodes
32802
2889
1329
0156

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (- x 1)) (cbrt (- x 1)))
0.3b
(* (cbrt (- x 1)) (cbrt (- x 1)))
30.5b
(fma x (/ 1 (+ x 1)) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
34.0b
(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
80×cbrt-prod
76×add-sqr-sqrt
60×*-un-lft-identity
28×swap-sqr
24×cbrt-div
20×associate-*r* associate-*l* add-cube-cbrt difference-of-squares
18×pow1
12×flip3-- pow1/3 difference-of-sqr-1 flip-- distribute-lft-out--
8×frac-times add-exp-log unswap-sqr
4×expm1-log1p-u add-cbrt-cube pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
2×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 156
Calls
4 calls:
47.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
38.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
0.0ms
(fma x (/ 1 (+ x 1)) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
0.0ms
(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
55.0ms
(* (cbrt (- x 1)) (cbrt (- x 1)))
155.0ms
(fma x (/ 1 (+ x 1)) (- (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))))))
288.0ms
(fma (- (/ (+ x 1) (cbrt (- x 1)))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (+ x 1) (cbrt (- x 1))) (/ 1 (* (cbrt (- x 1)) (cbrt (- x 1))))))

simplify2.0s

Counts
168 → 168
Iterations
IterNodes
33062
2974
1376
0175

prune2.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch189.0ms

Steps
ItersRangePoint
9
3862.7483140020904
127843612219.27428
9656.080272906422
10
-1231591086050.0088
-0.0006858147917088189
-7803.196355276564

simplify8.0ms

Iterations
IterNodes
348
248
143
029

end0.0ms

sample2.5s

Algorithm
intervals
Results
807.0ms1686×body1280valid
570.0ms601×body320valid
482.0ms4134×body80valid
451.0ms1276×body640valid
50.0ms303×body160valid