Details

Time bar (total: 17.6s)

sample58.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
15.0ms239×body80nan

simplify7.0ms

Calls
1 calls:
Slowest
6.0ms
(/ a (- (acos a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 1 expressions with local error:

0.2b
(/ a (- (acos a)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-/r*
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×distribute-lft-neg-in distribute-rgt-neg-in
1×expm1-log1p-u pow1 clear-num neg-mul-1 frac-2neg add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv add-log-exp
Calls
1 calls:
Slowest
2.0ms
(/ a (- (acos a)))

series27.0ms

Calls
1 calls:
Slowest
27.0ms
(/ a (- (acos a)))

simplify157.0ms

Calls
13 calls:
Slowest
43.0ms
(* -1 (/ a (acos a)))
38.0ms
(* -1 (/ a (acos a)))
38.0ms
(* -1 (/ a (acos a)))
6.0ms
(- (sqrt (acos a)))
6.0ms
(- (cbrt (acos a)))

prune185.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-/l*
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×associate-/r*
3×distribute-lft-neg-in pow1 distribute-rgt-neg-in add-exp-log div-inv
2×expm1-log1p-u clear-num frac-2neg add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
1×neg-sub0 rec-exp neg-mul-1 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Calls
2 calls:
Slowest
5.0ms
(/ (- (acos a)) a)
2.0ms
(/ 1 (/ (- (acos a)) a))

series55.0ms

Calls
2 calls:
Slowest
34.0ms
(/ (- (acos a)) a)
21.0ms
(/ 1 (/ (- (acos a)) a))

simplify306.0ms

Calls
20 calls:
Slowest
42.0ms
(* -1 (/ a (acos a)))
40.0ms
(* -1 (/ (acos a) a))
36.0ms
(* -1 (/ a (acos a)))
35.0ms
(* -1 (/ (acos a) a))
25.0ms
(* -1 (/ a (acos a)))

prune391.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (/ 1 (- (acos a))) (/ 1 a))
0.0b
(/ 1 (- (acos a)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
16×times-frac
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
14×associate-/r*
12×div-inv
7×add-exp-log
4×add-cbrt-cube associate-/l*
3×distribute-lft-neg-in pow1 distribute-rgt-neg-in
2×expm1-log1p-u rec-exp clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv neg-mul-1 associate-/r/ pow-flip inv-pow associate-/l/
Calls
2 calls:
Slowest
5.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
2.0ms
(/ 1 (- (acos a)))

series31.0ms

Calls
2 calls:
Slowest
21.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
11.0ms
(/ 1 (- (acos a)))

simplify2.9s

Calls
58 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
124.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
121.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
103.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
103.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune550.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
1.0b
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))
1.0b
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
0.4b
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
44×pow1
42×add-exp-log
26×pow-prod-up
22×prod-exp
21×pow-flip inv-pow
20×cbrt-div
19×frac-times associate-*l/
17×add-sqr-sqrt rec-exp *-un-lft-identity add-cube-cbrt
16×times-frac
12×add-cbrt-cube
10×pow-prod-down associate-*r/ un-div-inv associate-/l/
9×div-inv
8×associate-*r*
6×cbrt-prod pow-plus
5×associate-*l*
4×expm1-log1p-u associate-/r* cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow2
2×pow3 *-commutative
1×cbrt-undiv clear-num frac-2neg pow1/3 div-exp associate-/r/ rem-cbrt-cube
Calls
4 calls:
Slowest
30.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
12.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
11.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
6.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

series224.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
66.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
33.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
20.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify9.8s

Calls
167 calls:
Slowest
1.3s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
564.0ms
(* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
333.0ms
(* (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (* (/ 1 (- (acos a))) (/ 1 (- (acos a))))) (* (/ 1 (- (acos a))) (/ 1 (- (acos a))))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
318.0ms
(* (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
198.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
657.0ms8000×body80valid
432.0ms7904×body80nan