Details

Time bar (total: 13.3s)

sample41.0ms

Algorithm
intervals
Results
12.0ms250×body80nan
11.0ms256×body80valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04171
done4171

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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 log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
11.0ms
(/ a (- (acos a)))

series49.0ms

Counts
1 → 3
Calls
1 calls:
49.0ms
(/ a (- (acos a)))

simplify1.6s

Counts
60 → 60
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
09619614
117318814
246618734
3209318734
done500018734

prune296.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

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 log1p-expm1-u add-log-exp
1×neg-sub0 div-sub distribute-frac-neg associate-/r/ pow-flip inv-pow
Counts
2 → 221
Calls
2 calls:
11.0ms
(/ (- (acos a)) a)
22.0ms
(/ 1 (/ (- (acos a)) a))

series82.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(/ (- (acos a)) a)
35.0ms
(/ 1 (/ (- (acos a)) a))

simplify2.5s

Counts
227 → 227
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
029298276
179081641
2397781185
done500181185

prune753.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite92.0ms

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 log1p-expm1-u add-log-exp
1×associate-/r/ pow-flip inv-pow associate-/l/
Counts
2 → 584
Calls
2 calls:
7.0ms
(/ 1 (- (acos a)))
33.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

series58.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(/ 1 (- (acos a)))
47.0ms
(/ (/ 1 (- (acos a))) (/ 1 a))

simplify3.1s

Counts
590 → 590
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0811366342
12950276973
done5001254052

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac
144×*-un-lft-identity
143×add-sqr-sqrt
140×add-cube-cbrt
105×cbrt-prod
30×pow1
27×div-inv
20×associate-*r* add-exp-log
17×distribute-rgt-neg-in
15×distribute-lft-neg-in
14×add-cbrt-cube
13×associate-/r*
12×swap-sqr
11×associate-*l*
10×associate-/l*
7×pow-plus pow-prod-up
6×div-exp
5×neg-mul-1
4×distribute-lft-neg-out expm1-log1p-u pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow2 cbrt-undiv pow-sqr distribute-rgt-neg-out
2×cbrt-div *-commutative unswap-sqr
1×rec-exp clear-num frac-2neg pow1/3 1-exp pow3 sqr-neg associate-/r/ associate-/l/
Counts
4 → 284
Calls
4 calls:
20.0ms
(* (- (acos a)) (- (acos a)))
25.0ms
(/ (cbrt (/ 1 (* (* (- (acos a)) (- (acos a))) (- (acos a))))) (/ 1 a))
42.0ms
(* (* (- (acos a)) (- (acos a))) (- (acos a)))
66.0ms
(cbrt (/ 1 (* (* (- (acos a)) (- (acos a))) (- (acos a)))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (- (acos a)) (- (acos a)))
94.0ms
(/ (cbrt (/ 1 (* (* (- (acos a)) (- (acos a))) (- (acos a))))) (/ 1 a))
93.0ms
(* (* (- (acos a)) (- (acos a))) (- (acos a)))
81.0ms
(cbrt (/ 1 (* (* (- (acos a)) (- (acos a))) (- (acos a)))))

simplify1.1s

Counts
296 → 296
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0371172532
11037147774
done5001139297

prune963.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes85.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04171
done4171

end0.0ms

sample904.0ms

Algorithm
intervals
Results
353.0ms8000×body80valid
264.0ms8142×body80nan