Details

Time bar (total: 30.4s)

sample37.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
13.0ms240×body80nan

simplify4.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
3.0ms
(/ a (- (acos a)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 1 expressions with local error:

0.3b
(/ 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)))

series31.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
31.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 61
Calls
77 calls:
Slowest
194.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
65.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
56.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
39.0ms
(* -1 (/ a (acos a)))
32.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))

prune507.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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
11.0ms
(/ 1 (/ (- (acos a)) a))
6.0ms
(/ (- (acos a)) a)

series83.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
53.0ms
(/ (- (acos a)) a)
30.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.6s

Counts
326 → 229
Calls
326 calls:
Slowest
470.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
438.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
417.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
385.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
383.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

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
27.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
24.0ms
(* (- (acos a)) (/ 1 a))

series75.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
41.0ms
(* (- (acos a)) (/ 1 a))
34.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify3.2s

Counts
64 → 96
Calls
64 calls:
Slowest
421.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
214.0ms
(- 0 (log (* (- (acos a)) (/ 1 a))))
197.0ms
(- (log 1) (log (* (- (acos a)) (/ 1 a))))
175.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))
172.0ms
(/ (* (* 1 1) 1) (* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (/ (* (* 1 1) 1) (* (* a a) a))))

prune670.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ 1 a))
0.5b
(cbrt (/ 1 a))
0.5b
(cbrt (/ 1 a))
0.5b
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
119×cbrt-prod
97×add-sqr-sqrt
79×times-frac
67×*-un-lft-identity
57×add-cube-cbrt
18×swap-sqr
16×associate-*r* associate-*l* unswap-sqr
11×pow1
9×pow1/3 div-inv
7×cbrt-div
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 → 165
Calls
4 calls:
Slowest
11.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
2.0ms
(cbrt (/ 1 a))
1.0ms
(cbrt (/ 1 a))
1.0ms
(cbrt (/ 1 a))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
345.0ms
(cbrt (/ 1 a))
344.0ms
(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
307.0ms
(cbrt (/ 1 a))
280.0ms
(cbrt (/ 1 a))

simplify3.6s

Counts
170 → 177
Calls
170 calls:
Slowest
438.0ms
(* (pow (/ 1 (pow a 2)) 1/3) (pow (cbrt -1) 2))
179.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
137.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
115.0ms
(* (pow (/ -1 a) 1/3) (cbrt -1))
94.0ms
(* (* (cbrt (cbrt (/ 1 a))) (cbrt (cbrt (/ 1 a)))) (* (cbrt (cbrt (/ 1 a))) (cbrt (cbrt (/ 1 a)))))

prune1.8s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes125.0ms

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
629.0ms8000×body80valid
443.0ms8060×body80nan