Details

Time bar (total: 13.5s)

sample40.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
12.0ms228×body80nan

simplify6.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite2.0ms

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×pow1 clear-num neg-mul-1 frac-2neg add-cbrt-cube add-exp-log insert-posit16 div-inv add-log-exp
Calls
1 calls:
Slowest
2.0ms
(/ a (- (acos a)))

series23.0ms

Calls
1 calls:
Slowest
23.0ms
(/ a (- (acos a)))

simplify143.0ms

Calls
13 calls:
Slowest
35.0ms
(* -1 (/ a (acos a)))
34.0ms
(* -1 (/ a (acos a)))
20.0ms
(* -1 (/ a (acos a)))
14.0ms
(- (cbrt (acos a)))
6.0ms
(- (sqrt (acos a)))

prune148.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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×clear-num frac-2neg add-cbrt-cube insert-posit16 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))

series34.0ms

Calls
2 calls:
Slowest
18.0ms
(/ 1 (/ (- (acos a)) a))
16.0ms
(/ (- (acos a)) a)

simplify226.0ms

Calls
20 calls:
Slowest
39.0ms
(* -1 (/ a (acos a)))
32.0ms
(* -1 (/ a (acos a)))
25.0ms
(* -1 (/ (acos a) a))
25.0ms
(* -1 (/ (acos a) a))
18.0ms
(* -1 (/ a (acos a)))

prune270.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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×rec-exp clear-num frac-2neg div-exp insert-posit16 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))
1.0ms
(/ 1 (- (acos a)))

series21.0ms

Calls
2 calls:
Slowest
14.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify2.1s

Calls
58 calls:
Slowest
955.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
104.0ms
(- (log (/ 1 (- (acos a)))) (log (/ 1 a)))
87.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
81.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
63.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

prune367.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite67.0ms

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×associate-/r* cbrt-unprod insert-posit16 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
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))
11.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
11.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))

series162.0ms

Calls
4 calls:
Slowest
62.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
58.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
28.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
13.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify7.1s

Calls
167 calls:
Slowest
933.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
379.0ms
(* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
312.0ms
(* (* (* (* (/ 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)))))
275.0ms
(* (* (* (* (/ 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)))))
139.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
811.0ms7955×body80nan
523.0ms8000×body80valid