Details

Time bar (total: 2.2m)

sample33.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
10.0ms241×body80nan

simplify3.0ms

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

prune4.0ms

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)))

rewrite11.0ms

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)))

series52.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
52.0ms
(/ a (- (acos a)))

simplify1.6s

Counts
92 → 61
Calls
92 calls:
Slowest
346.0ms
(* (* (/ a (- (acos a))) (/ a (- (acos a)))) (/ a (- (acos a))))
207.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
100.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
51.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
40.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))

prune423.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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
15.0ms
(/ 1 (/ (- (acos a)) a))
10.0ms
(/ (- (acos a)) a)

series66.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
35.0ms
(/ (- (acos a)) a)
31.0ms
(/ 1 (/ (- (acos a)) a))

simplify17.6s

Counts
363 → 229
Calls
363 calls:
Slowest
827.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
541.0ms
(* (* (/ 1 (/ (- (acos a)) a)) (/ 1 (/ (- (acos a)) a))) (/ 1 (/ (- (acos a)) a)))
497.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
434.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
419.0ms
(* (* (/ (- (acos a)) a) (/ (- (acos a)) a)) (/ (- (acos a)) a))

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
1207×times-frac
550×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
138×distribute-lft-neg-in distribute-rgt-neg-in
51×div-inv
46×neg-mul-1 add-exp-log
37×associate-/l*
34×div-exp
23×associate-/r*
16×add-cbrt-cube
9×cbrt-undiv rec-exp 1-exp
3×pow1
2×expm1-log1p-u clear-num frac-2neg insert-posit16 log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 586
Calls
2 calls:
Slowest
11.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
5.0ms
(/ 1 (- (acos a)))

series68.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.6m

Counts
1065 → 592
Calls
1065 calls:
Slowest
943.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
704.0ms
(/ (/ 1 (* (cbrt (- (acos a))) (cbrt (- (acos a))))) (/ 1 (* (cbrt a) (cbrt a))))
677.0ms
(/ (/ 1 (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
659.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
644.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (sqrt a)))

prune3.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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
14.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))
11.0ms
(* (- (acos a)) (/ 1 a))

series81.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
56.0ms
(* (- (acos a)) (/ 1 a))
25.0ms
(/ 1 (* (- (acos a)) (/ 1 a)))

simplify6.4s

Counts
100 → 96
Calls
100 calls:
Slowest
428.0ms
(* (* (/ 1 (* (- (acos a)) (/ 1 a))) (/ 1 (* (- (acos a)) (/ 1 a)))) (/ 1 (* (- (acos a)) (/ 1 a))))
366.0ms
(* (* (* (- (acos a)) (/ 1 a)) (* (- (acos a)) (/ 1 a))) (* (- (acos a)) (/ 1 a)))
337.0ms
(* (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
237.0ms
(exp (* (- (acos a)) (/ 1 a)))
219.0ms
(* (- (acos a)) (/ (sqrt 1) (* (cbrt a) (cbrt a))))

prune388.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample909.0ms

Algorithm
intervals
Results
455.0ms8000×body80valid
277.0ms8062×body80nan