Details

Time bar (total: 3.9m)

sample33.0ms

Algorithm
intervals
Results
11.0ms58×body640valid
7.0ms136×body80valid
5.0ms36×body320valid
3.0ms26×body160valid

simplify18.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
18.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize44.0ms

Local error

Found 3 expressions with local error:

2.7b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
850×*-un-lft-identity
783×times-frac
710×add-sqr-sqrt
486×prod-diff
454×add-cube-cbrt
125×difference-of-squares
98×associate-/r/
94×distribute-lft-out
81×distribute-lft-out--
58×difference-of-sqr-1
52×div-inv
30×flip-+
29×flip3-+
21×flip--
20×flip3--
18×fma-neg
11×associate-/r* add-exp-log
7×add-cbrt-cube
6×associate-/l*
5×pow1 add-log-exp
4×div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
1×sub-neg diff-log frac-sub
Counts
3 → 638
Calls
3 calls:
Slowest
99.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
19.0ms
(/ 1 (+ x 1))
18.0ms
(/ 1 (- x 1))

series103.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
74.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
15.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

simplify3.5m

Counts
1141 → 647
Calls
1141 calls:
Slowest
898.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
888.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
819.0ms
(fma (- (/ (sqrt 1) (- (sqrt x) (sqrt 1)))) (/ (sqrt 1) (+ (sqrt x) (sqrt 1))) (* (/ (sqrt 1) (- (sqrt x) (sqrt 1))) (/ (sqrt 1) (+ (sqrt x) (sqrt 1)))))
780.0ms
(fma (/ 1 (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ 1 (- (* x x) (* 1 1))))))
745.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ (sqrt 1) (- (sqrt x) (sqrt 1))) (/ (sqrt 1) (+ (sqrt x) (sqrt 1))))))

prune5.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1 (fma x x -1))
0.0b
(* (/ 1 (fma x x -1)) -2)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log
13×associate-*l*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp
3×associate-/r* associate-*r* associate-/l* unswap-sqr
2×expm1-log1p-u cbrt-undiv rec-exp 1-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative pow-flip inv-pow
Counts
2 → 72
Calls
2 calls:
Slowest
10.0ms
(* (/ 1 (fma x x -1)) -2)
4.0ms
(/ 1 (fma x x -1))

series122.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(/ 1 (fma x x -1))
56.0ms
(* (/ 1 (fma x x -1)) -2)

simplify5.5s

Counts
60 → 78
Calls
60 calls:
Slowest
1.1s
(* (* (* (/ 1 (fma x x -1)) (/ 1 (fma x x -1))) (/ 1 (fma x x -1))) (* (* -2 -2) -2))
401.0ms
(* (/ (* (* 1 1) 1) (* (* (fma x x -1) (fma x x -1)) (fma x x -1))) (* (* -2 -2) -2))
323.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
285.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
247.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))

prune627.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

14.5b
(cbrt (/ 1 (fma x x -1)))
14.5b
(cbrt (/ 1 (fma x x -1)))
14.5b
(cbrt (/ 1 (fma x x -1)))
0.4b
(/ 1 (fma x x -1))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
36×times-frac
33×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-exp-log
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-div associate-/r* pow1/3 associate-/l*
2×div-exp
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
Counts
4 → 109
Calls
4 calls:
Slowest
8.0ms
(/ 1 (fma x x -1))
3.0ms
(cbrt (/ 1 (fma x x -1)))
3.0ms
(cbrt (/ 1 (fma x x -1)))
3.0ms
(cbrt (/ 1 (fma x x -1)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(cbrt (/ 1 (fma x x -1)))
174.0ms
(cbrt (/ 1 (fma x x -1)))
165.0ms
(cbrt (/ 1 (fma x x -1)))
36.0ms
(/ 1 (fma x x -1))

simplify5.8s

Counts
81 → 121
Calls
81 calls:
Slowest
389.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
307.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
292.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
291.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
278.0ms
(+ (pow (/ -1 x) 2/3) (+ (* 2/9 (pow (/ 1 (pow x 14)) 1/3)) (* 1/3 (pow (/ 1 (pow x 8)) 1/3))))

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

15.0b
(cbrt (fma x x -1))
14.5b
(cbrt (/ 1 (fma x x -1)))
14.5b
(cbrt (/ 1 (fma x x -1)))
0.4b
(/ 1 (fma x x -1))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
29×cbrt-prod
27×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
8×add-exp-log
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* pow1/3 div-inv associate-/l*
2×cbrt-div div-exp
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
Counts
4 → 98
Calls
4 calls:
Slowest
8.0ms
(/ 1 (fma x x -1))
3.0ms
(cbrt (/ 1 (fma x x -1)))
3.0ms
(cbrt (/ 1 (fma x x -1)))
2.0ms
(cbrt (fma x x -1))

series584.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(cbrt (/ 1 (fma x x -1)))
156.0ms
(cbrt (fma x x -1))
156.0ms
(cbrt (/ 1 (fma x x -1)))
60.0ms
(/ 1 (fma x x -1))

simplify5.2s

Counts
70 → 110
Calls
70 calls:
Slowest
404.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
301.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
287.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
282.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
259.0ms
(- (pow (/ -1 x) -2/3) (+ (* 1/9 (pow (/ 1 (pow x 10)) 1/3)) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))))

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes29.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
599.0ms1849×body640valid
374.0ms1245×body320valid
346.0ms4313×body80valid
81.0ms593×body160valid