Details

Time bar (total: 1.5m)

sample158.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
14.0ms249×body80nan

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1 x) (+ 1 x))
0.0b
(atan (sqrt (/ (- 1 x) (+ 1 x))))
0.0b
(sqrt (/ (- 1 x) (+ 1 x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
56×add-sqr-sqrt
49×times-frac
30×sqrt-prod
26×add-cube-cbrt
18×difference-of-squares
13×distribute-lft-out
9×distribute-lft-out--
6×associate-/l*
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
3 → 109
Calls
3 calls:
Slowest
17.0ms
(/ (- 1 x) (+ 1 x))
11.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series87.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
44.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
38.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.6s

Counts
106 → 118
Calls
106 calls:
Slowest
487.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
264.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
205.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
199.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
145.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x)))))
0.0b
(/ (- 1 x) (sqrt (+ 1 x)))
0.0b
(sqrt (+ 1 x))
0.0b
(sqrt (+ 1 x))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
199×sqrt-prod
187×add-sqr-sqrt
155×*-un-lft-identity
133×times-frac
64×add-cube-cbrt
51×associate-*r*
30×associate-*l* difference-of-squares
24×unswap-sqr
18×distribute-lft-out
15×distribute-lft-out--
14×sqrt-div
10×pow1
8×add-cbrt-cube add-exp-log
7×associate-/r*
6×associate-/r/ associate-/l*
5×flip3-+ flip-+
4×expm1-log1p-u sqrt-pow1 pow1/2 hypot-def insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square hypot-1-def associate-/l/
1×frac-times cbrt-undiv clear-num frac-2neg flip3-- sqrt-unprod div-sub div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip--
Counts
4 → 244
Calls
4 calls:
Slowest
70.0ms
(* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x)))))
21.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
5.0ms
(sqrt (+ 1 x))
5.0ms
(sqrt (+ 1 x))

series218.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
64.0ms
(* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x)))))
38.0ms
(sqrt (+ 1 x))
38.0ms
(sqrt (+ 1 x))

simplify9.6s

Counts
271 → 256
Calls
271 calls:
Slowest
401.0ms
(* (* (* (sqrt (/ 1 (sqrt (+ 1 x)))) (sqrt (/ 1 (sqrt (+ 1 x))))) (sqrt (/ 1 (sqrt (+ 1 x))))) (* (* (sqrt (/ (- 1 x) (sqrt (+ 1 x)))) (sqrt (/ (- 1 x) (sqrt (+ 1 x))))) (sqrt (/ (- 1 x) (sqrt (+ 1 x))))))
337.0ms
(* (/ 1 (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
321.0ms
(* (/ 1 (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
290.0ms
(* (/ 1 (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
259.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))

prune3.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))
0.0b
(* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))))
0.0b
(cbrt (* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))))))
0.0b
(/ (- 1 x) (sqrt (+ x 1)))

rewrite350.0ms

Algorithm
rewrite-expression-head
Rules
836×sqrt-prod
777×times-frac
757×*-un-lft-identity
531×add-sqr-sqrt
318×add-cube-cbrt
142×difference-of-squares
113×distribute-lft-out
71×distribute-lft-out--
57×associate-/l*
48×associate-*l*
31×sqrt-div
29×add-cbrt-cube add-exp-log
22×associate-/r/
14×associate-/r*
11×flip3-+ flip-+ div-inv
10×frac-times prod-exp associate-*r/ cbrt-unprod
9×pow1
7×cbrt-undiv cbrt-div div-exp
6×associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down associate-/l/
2×clear-num frac-2neg
1×cbrt-prod sqrt-undiv flip3-- pow1/3 div-sub associate-*r* *-commutative flip--
Counts
4 → 609
Calls
4 calls:
Slowest
143.0ms
(* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))))
102.0ms
(cbrt (* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))))))
52.0ms
(/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))
34.0ms
(/ (- 1 x) (sqrt (+ x 1)))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
172.0ms
(/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))
92.0ms
(* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))))
67.0ms
(/ (- 1 x) (sqrt (+ x 1)))
61.0ms
(cbrt (* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))))))

simplify43.5s

Counts
971 → 621
Calls
971 calls:
Slowest
894.0ms
(* (/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1))))) (sqrt (/ 1 (sqrt (+ x 1))))) (/ (* (* (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (/ (- 1 x) (sqrt (+ x 1))))) (sqrt (/ (- 1 x) (sqrt (+ x 1))))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))))
772.0ms
(* (* (* (/ (- 1 x) (sqrt (+ x 1))) (/ (- 1 x) (sqrt (+ x 1)))) (/ (- 1 x) (sqrt (+ x 1)))) (* (* (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1))))) (sqrt (/ 1 (sqrt (+ x 1))))) (/ (* (* (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (/ (- 1 x) (sqrt (+ x 1))))) (sqrt (/ (- 1 x) (sqrt (+ x 1))))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))))
647.0ms
(* (/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))))))
546.0ms
(* (/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1))))) (sqrt (/ 1 (sqrt (+ x 1))))) (* (* (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1))))))
512.0ms
(* (/ (- 1 x) (sqrt (+ x 1))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (/ (sqrt (/ (- 1 x) (sqrt (+ x 1)))) (sqrt (+ x 1)))))

prune10.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (/ (- 1 x) (+ 1 x)))
0.0b
(cbrt (/ (- 1 x) (+ 1 x)))
0.0b
(cbrt (/ (- 1 x) (+ 1 x)))
0.0b
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
365×*-un-lft-identity
270×cbrt-prod
222×times-frac
213×add-sqr-sqrt
93×add-cube-cbrt
64×difference-of-squares
62×distribute-lft-out
57×swap-sqr
44×distribute-lft-out--
33×associate-*r* associate-*l*
14×associate-/r/
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div flip3-+ flip-+ div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 282
Calls
4 calls:
Slowest
76.0ms
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))
5.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
5.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
5.0ms
(cbrt (/ (- 1 x) (+ 1 x)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
90.0ms
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))
72.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
70.0ms
(cbrt (/ (- 1 x) (+ 1 x)))

simplify11.4s

Counts
319 → 294
Calls
319 calls:
Slowest
698.0ms
(* (/ (- 1 x) (+ 1 x)) (/ (- 1 x) (+ 1 x)))
343.0ms
(* (/ (- 1 x) (+ 1 x)) (/ (- 1 x) (+ 1 x)))
213.0ms
(* (cbrt (/ (- 1 x) (+ (pow 1 3) (pow x 3)))) (cbrt (/ (- 1 x) (+ (pow 1 3) (pow x 3)))))
213.0ms
(cbrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
212.0ms
(cbrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))

prune4.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes68.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.0s8000×body80valid
784.0ms7941×body80nan