Details

Time bar (total: 25.8s)

sample29.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
10.0ms293×body80nan

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
4.0ms
(/ a (- (acos a)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 58
Calls
1 calls:
Slowest
10.0ms
(/ a (- (acos a)))

series36.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
36.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 61
Calls
77 calls:
Slowest
249.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
80.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
62.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
49.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
32.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))

prune433.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ 1 (/ (- (acos a)) a))
0.3b
(/ (- (acos a)) a)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
140×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
48×distribute-lft-neg-in distribute-rgt-neg-in
37×associate-/r*
16×neg-mul-1
15×add-exp-log
13×associate-/l*
9×add-cbrt-cube
8×div-exp
6×div-inv
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp clear-num frac-2neg 1-exp insert-posit16 log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 223
Calls
2 calls:
Slowest
8.0ms
(/ (- (acos a)) a)
7.0ms
(/ 1 (/ (- (acos a)) a))

series74.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
39.0ms
(/ (- (acos a)) a)
35.0ms
(/ 1 (/ (- (acos a)) a))

simplify15.0s

Counts
326 → 229
Calls
326 calls:
Slowest
557.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
482.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
381.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
331.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
322.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ 1 (* (- (acos a)) (/ 1 a)))
0.3b
(* (- (acos a)) (/ 1 a))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
21×add-sqr-sqrt
18×div-exp
16×add-cbrt-cube prod-exp
15×*-un-lft-identity
14×times-frac add-cube-cbrt
13×associate-*r*
10×associate-*l*
9×rec-exp 1-exp
7×pow1
5×cbrt-undiv
4×cbrt-unprod
3×distribute-lft-neg-in distribute-rgt-neg-in associate-/l* unswap-sqr
2×expm1-log1p-u pow-prod-down associate-*r/ associate-/r/ un-div-inv insert-posit16 log1p-expm1-u div-inv pow-flip add-log-exp
1×distribute-lft-neg-out clear-num associate-/r* neg-mul-1 frac-2neg *-commutative inv-pow
Counts
2 → 90
Calls
2 calls:
Slowest
15.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
14.0ms
(* (- (acos a)) (/ 1 a))

series68.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
41.0ms
(* (- (acos a)) (/ 1 a))
27.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify3.1s

Counts
64 → 96
Calls
64 calls:
Slowest
359.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
193.0ms
(- 0 (log (* (- (acos a)) (/ 1 a))))
191.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a))))
169.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a))))
167.0ms
(- (log 1) (log (* (- (acos a)) (/ 1 a))))

prune578.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.9b
(sqrt (acos a))
0.9b
(sqrt (acos a))
0.6b
(cbrt a)
0.6b
(cbrt a)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
Slowest
2.0ms
(sqrt (acos a))
2.0ms
(sqrt (acos a))
1.0ms
(cbrt a)
1.0ms
(cbrt a)

series628.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
307.0ms
(cbrt a)
297.0ms
(cbrt a)
13.0ms
(sqrt (acos a))
11.0ms
(sqrt (acos a))

simplify424.0ms

Counts
28 → 72
Calls
28 calls:
Slowest
158.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
130.0ms
(* (pow (* a -1) 1/3) (cbrt -1))
32.0ms
(pow (/ 1 a) -1/3)
24.0ms
(pow (/ 1 a) -1/3)
8.0ms
(sqrt (* (cbrt (acos a)) (cbrt (acos a))))

prune694.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
790.0ms8001×body80nan
613.0ms8000×body80valid