Details

Time bar (total: 14.8s)

sample53.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
17.0ms284×body80nan

simplify3.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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×pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 div-inv add-log-exp
Counts
1 → 56
Calls
1 calls:
Slowest
6.0ms
(/ a (- (acos a)))

series46.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
46.0ms
(/ a (- (acos a)))

simplify1.3s

Counts
59 → 59

prune508.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (- (acos a)) a)
0.2b
(/ 1 (/ (- (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×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 219
Calls
2 calls:
Slowest
12.0ms
(/ 1 (/ (- (acos a)) a))
7.0ms
(/ (- (acos a)) a)

series78.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
49.0ms
(/ (- (acos a)) a)
29.0ms
(/ 1 (/ (- (acos a)) a))

simplify869.0ms

Counts
225 → 225

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (- (acos a)) (/ 1 a))
0.2b
(/ 1 (* (- (acos a)) (/ 1 a)))

rewrite52.0ms

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×pow-prod-down associate-*r/ associate-/r/ un-div-inv insert-posit16 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 → 86
Calls
2 calls:
Slowest
27.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
23.0ms
(* (- (acos a)) (/ 1 a))

series101.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
58.0ms
(* (- (acos a)) (/ 1 a))
43.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify1.3s

Counts
92 → 92

prune754.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(cbrt (/ (- (acos a)) a))
0.5b
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
262×cbrt-prod
228×times-frac
176×add-sqr-sqrt
164×*-un-lft-identity
152×add-cube-cbrt
69×distribute-rgt-neg-in
63×distribute-lft-neg-in
43×swap-sqr
37×associate-*r* associate-*l*
21×neg-mul-1
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×add-cbrt-cube insert-posit16 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 → 280
Calls
4 calls:
Slowest
18.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
2.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))
2.0ms
(cbrt (/ (- (acos a)) a))

series980.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
279.0ms
(* (cbrt (/ (- (acos a)) a)) (cbrt (/ (- (acos a)) a)))
248.0ms
(cbrt (/ (- (acos a)) a))
232.0ms
(cbrt (/ (- (acos a)) a))
219.0ms
(cbrt (/ (- (acos a)) a))

simplify1.3s

Counts
292 → 292

prune3.9s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0b

regimes187.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
673.0ms8000×body80valid
486.0ms8133×body80nan