Details

Time bar (total: 2.3m)

sample54.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
16.0ms268×body80nan

simplify6.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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×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
6.0ms
(/ a (- (acos a)))

series34.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
34.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 61
Calls
77 calls:
Slowest
218.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
76.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
61.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (- (acos a))) (cbrt (- (acos a)))))
38.0ms
(* -1 (/ a (acos a)))
37.0ms
(/ 1 (- (* (cbrt (acos a)) (cbrt (acos a)))))

prune384.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite33.0ms

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
14.0ms
(/ 1 (/ (- (acos a)) a))
12.0ms
(/ (- (acos a)) a)

series107.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
65.0ms
(/ (- (acos a)) a)
42.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.9s

Counts
326 → 229
Calls
326 calls:
Slowest
597.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
477.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
349.0ms
(/ (sqrt 1) (/ (* (cbrt (acos a)) (cbrt (acos a))) (* (cbrt a) (cbrt a))))
345.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
332.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite54.0ms

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
22.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

series43.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
6.0ms
(/ 1 (- (acos a)))

simplify1.4m

Counts
1031 → 592
Calls
1031 calls:
Slowest
1.2s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
1.1s
(/ (/ (sqrt 1) (- (sqrt (acos a)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
891.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (/ (* (* 1 1) 1) (* (* a a) a)))
667.0ms
(/ (/ (sqrt 1) (- (sqrt (acos a)))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
623.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (acos a)) (cbrt (acos a)))) (/ 1 (* (cbrt a) (cbrt a))))

prune2.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize24.0ms

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))))
0.9b
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
0.4b
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
302×add-exp-log
273×times-frac
185×add-sqr-sqrt
178×*-un-lft-identity
157×add-cube-cbrt
148×prod-exp
120×div-exp
68×associate-*r*
60×add-cbrt-cube
59×pow1
58×rec-exp 1-exp
51×distribute-rgt-neg-in
45×distribute-lft-neg-in
42×swap-sqr
35×associate-*l*
31×pow-prod-up
29×pow-flip inv-pow
22×cbrt-unprod
20×cbrt-undiv cbrt-div
19×frac-times associate-*l/
15×cbrt-prod neg-mul-1
13×associate-/r* div-inv
12×unswap-sqr
10×pow-prod-down associate-*r/ un-div-inv associate-/l/
9×pow-sqr
7×pow-plus
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×pow2
2×pow3 *-commutative
1×clear-num frac-2neg pow1/3 associate-/r/ rem-cbrt-cube
Counts
4 → 451
Calls
4 calls:
Slowest
45.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
30.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
18.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))
7.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))

series162.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
71.0ms
(/ (cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ 1 a))
38.0ms
(cbrt (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
33.0ms
(* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))
21.0ms
(* (/ 1 (- (acos a))) (/ 1 (- (acos a))))

simplify30.2s

Counts
548 → 463
Calls
548 calls:
Slowest
831.0ms
(* (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a))))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
818.0ms
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
809.0ms
(* (* (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a))))) (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))))
809.0ms
(* (* (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a))))) (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))))
684.0ms
(* (* (* (* (/ 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)))))

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes51.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample899.0ms

Algorithm
intervals
Results
399.0ms8000×body80valid
316.0ms8098×body80nan