Details

Time bar (total: 3.1m)

sample53.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
15.0ms249×body80nan

simplify7.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
7.0ms
(/ a (- (acos a)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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
5.0ms
(/ a (- (acos a)))

series50.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
50.0ms
(/ a (- (acos a)))

simplify1.1s

Counts
77 → 61
Calls
77 calls:
Slowest
195.0ms
(/ (* (* a a) a) (* (* (- (acos a)) (- (acos a))) (- (acos a))))
83.0ms
(/ (* (cbrt a) (cbrt a)) (- (* (cbrt (acos a)) (cbrt (acos a)))))
41.0ms
(/ (* (cbrt a) (cbrt a)) (* (cbrt (acos a)) (cbrt (acos a))))
36.0ms
(* -1 (/ a (acos a)))
34.0ms
(* -1 (/ a (acos a)))

prune405.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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

series99.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
62.0ms
(/ (- (acos a)) a)
37.0ms
(/ 1 (/ (- (acos a)) a))

simplify14.6s

Counts
326 → 229
Calls
326 calls:
Slowest
440.0ms
(/ (sqrt 1) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))
398.0ms
(/ (* (* 1 1) 1) (/ (* (* (- (acos a)) (- (acos a))) (- (acos a))) (* (* a a) a)))
391.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (- (acos a))) (cbrt (- (acos a)))) (* (cbrt a) (cbrt a))))
365.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (sqrt a)))
354.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (- (* (cbrt (acos a)) (cbrt (acos a)))) (* (cbrt a) (cbrt a))))

prune1.9s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

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
12.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
5.0ms
(/ 1 (- (acos a)))

series49.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
39.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))
10.0ms
(/ 1 (- (acos a)))

simplify1.5m

Counts
1031 → 592
Calls
1031 calls:
Slowest
1.1s
(/ (* (* (/ 1 (- (acos a))) (/ 1 (- (acos a)))) (/ 1 (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
1.1s
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ 1 (sqrt a)))
926.0ms
(/ (/ (* (* 1 1) 1) (* (* (- (acos a)) (- (acos a))) (- (acos a)))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
624.0ms
(/ (/ (sqrt 1) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
590.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (/ (sqrt 1) (sqrt a)))

prune3.7s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
1.0b
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
0.4b
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
0.0b
(* (acos a) (acos a))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
1965×times-frac
673×add-sqr-sqrt
671×*-un-lft-identity add-cube-cbrt
570×cbrt-prod
153×distribute-lft-neg-in distribute-rgt-neg-in
76×div-inv
75×associate-/l*
51×neg-mul-1
37×add-exp-log
21×add-cbrt-cube
18×div-exp
14×associate-/r*
11×pow1
9×cbrt-undiv
5×prod-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp swap-sqr associate-*r* associate-*l* cbrt-unprod
2×cbrt-div clear-num frac-2neg associate-/l/
1×pow2 pow-plus pow1/3 pow-prod-down associate-/r/ pow-sqr *-commutative pow-prod-up unswap-sqr
Counts
4 → 781
Calls
4 calls:
Slowest
19.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
15.0ms
(* (acos a) (acos a))
15.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
11.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(/ (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a)))) (/ 1 a))
69.0ms
(cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))
46.0ms
(/ (/ 1 (- (acos a))) (* (acos a) (acos a)))
15.0ms
(* (acos a) (acos a))

simplify1.2m

Counts
1311 → 793
Calls
1311 calls:
Slowest
611.0ms
(/ (/ (/ 1 (- (acos a))) (* (acos a) (acos a))) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
366.0ms
(/ (cbrt (cbrt (/ (/ 1 (- (acos a))) (* (acos a) (acos a))))) (/ (sqrt 1) (sqrt a)))
294.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a))))
279.0ms
(/ (cbrt (/ (/ (* (cbrt 1) (cbrt 1)) (- (* (cbrt (acos a)) (cbrt (acos a))))) (acos a))) (/ (sqrt 1) (* (cbrt a) (cbrt a))))
277.0ms
(/ (/ (/ 1 (- (acos a))) (* (acos a) (acos a))) (/ (* (* 1 1) 1) (* (* a a) a)))

prune5.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes60.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample890.0ms

Algorithm
intervals
Results
454.0ms8000×body80valid
293.0ms7941×body80nan