Details

Time bar (total: 4.1m)

sample65.0ms

Algorithm
intervals
Results
15.0ms288×body80nan
12.0ms50×body640valid
12.0ms39×body1280valid
9.0ms136×body80valid
4.0ms23×body320valid
1.0ms8×body160valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize35.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
902×*-un-lft-identity
788×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
580×sqrt-prod
74×distribute-lft-out
56×div-inv
48×sqrt-div
46×associate-/r/
25×difference-of-squares
24×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×pow-flip associate-/l* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp hypot-def inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 793
Calls
4 calls:
Slowest
29.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(sqrt (+ x 1))
5.0ms
(/ 1 (sqrt x))

series202.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
47.0ms
(/ 1 (sqrt (+ x 1)))
42.0ms
(/ 1 (sqrt x))
27.0ms
(sqrt (+ x 1))

simplify1.9m

Counts
1414 → 805
Calls
1414 calls:
Slowest
526.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
497.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
383.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
381.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))
371.0ms
(fma (- (/ (sqrt 1) (sqrt (cbrt (+ x 1))))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ (sqrt 1) (sqrt (cbrt (+ x 1)))) (/ (sqrt 1) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))

prune4.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.0b

localize33.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.5b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
426×times-frac
387×*-un-lft-identity
340×add-sqr-sqrt
208×sqrt-prod
176×add-cube-cbrt
98×distribute-lft-out
86×add-exp-log
71×swap-sqr
50×pow1 unswap-sqr
49×associate-*r* associate-*l*
48×pow-flip
33×div-exp div-inv
32×prod-exp frac-sub
30×add-cbrt-cube
18×frac-times associate-*l/ associate-*r/ un-div-inv pow-prod-up difference-of-squares associate-/l/
16×rec-exp associate-/r* sqrt-pow1 pow1/2 1-exp inv-pow
11×associate-/r/
10×pow-prod-down pow-sqr
9×cbrt-undiv
8×sqrt-div cbrt-unprod
6×add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
2×pow2 pow-plus flip3-- *-commutative flip--
1×clear-num sub-neg frac-2neg fma-neg diff-log div-sub prod-diff frac-add
Counts
4 → 486
Calls
4 calls:
Slowest
74.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
35.0ms
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
19.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
16.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
44.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
22.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
20.0ms
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))

simplify41.9s

Counts
675 → 498
Calls
675 calls:
Slowest
531.0ms
(/ (sqrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) 1)
421.0ms
(* (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))) (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))))
381.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
363.0ms
(* (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
355.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))

prune3.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (fma x x x))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
661×times-frac
618×*-un-lft-identity
260×add-sqr-sqrt add-cube-cbrt
228×distribute-lft-out
196×sqrt-prod
77×div-inv
32×associate-/r*
25×add-exp-log
22×associate-/l*
15×add-cbrt-cube
12×div-exp
9×pow1
7×pow-flip
6×cbrt-undiv
5×associate-/r/
4×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×inv-pow
2×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
1×frac-add associate-/l/
Counts
4 → 396
Calls
4 calls:
Slowest
38.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
11.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))
4.0ms
(/ 1 (fma x x x))

series226.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
28.0ms
(/ 1 (sqrt (+ x 1)))
28.0ms
(/ 1 (fma x x x))
28.0ms
(/ 1 (sqrt x))

simplify32.7s

Counts
600 → 408
Calls
600 calls:
Slowest
526.0ms
(/ (/ 1 (fma x x x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
303.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (fma x x x)) (cbrt (fma x x x)))) 1)
277.0ms
(/ (/ 1 (fma x x x)) (+ (/ (sqrt 1) (sqrt x)) (/ (sqrt 1) (sqrt (+ x 1)))))
276.0ms
(/ (/ 1 (fma x x x)) (+ (/ (sqrt 1) (sqrt x)) (/ (sqrt 1) (sqrt (+ x 1)))))
275.0ms
(/ (/ 1 (fma x x x)) (+ (/ (cbrt 1) (sqrt x)) (/ (cbrt 1) (sqrt (+ x 1)))))

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ x (sqrt x))
0.3b
(/ x (sqrt (+ 1 x)))
0.2b
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
0.0b
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
872×*-un-lft-identity
852×times-frac
332×distribute-lft-out
308×add-sqr-sqrt add-cube-cbrt
280×sqrt-prod
59×div-inv
37×associate-/r/
27×associate-/r* fma-def
24×associate-/l*
19×flip3-+ flip-+
17×add-exp-log
13×add-cbrt-cube
8×div-exp
7×pow1
6×add-log-exp
5×cbrt-undiv
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×frac-add pow-div
1×+-commutative rec-exp sum-log sqrt-pow1 pow1/2 1-exp associate-/l/
Counts
4 → 452
Calls
4 calls:
Slowest
47.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
31.0ms
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))
12.0ms
(/ x (sqrt (+ 1 x)))
5.0ms
(/ x (sqrt x))

series349.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
96.0ms
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))
52.0ms
(/ x (sqrt (+ 1 x)))
51.0ms
(/ x (sqrt x))

simplify40.3s

Counts
706 → 464
Calls
706 calls:
Slowest
465.0ms
(/ (/ (sqrt 1) (+ 1 x)) (+ (/ (cbrt x) (sqrt (+ 1 x))) (/ (cbrt x) (sqrt x))))
397.0ms
(/ (* (* x x) x) (* (* (sqrt x) (sqrt x)) (sqrt x)))
374.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) 1))
325.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) (sqrt 1)))
325.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) (sqrt 1)))

prune3.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes25.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
559.0ms1865×body640valid
475.0ms8044×body80nan
374.0ms1118×body1280valid
333.0ms4109×body80valid
125.0ms594×body320valid
58.0ms314×body160valid