Details

Time bar (total: 13.0s)

sample19.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
4.0ms272×body80nan

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
045
done45

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
30×times-frac
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/r*
4×neg-mul-1
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 57
Calls
1 calls:
4.0ms
(/ a (- (acos a)))

series24.0ms

Counts
1 → 3
Calls
1 calls:
24.0ms
(/ a (- (acos a)))

simplify3.0s

Counts
60 → 60
Iterations

Useful iterations: 5 (1.2s)

IterNodesCost
096613
1166581
2330563
3716563
41240563
52182558
done5000558

prune125.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
101×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×div-inv
8×add-exp-log
6×add-cbrt-cube associate-/l*
4×neg-mul-1
3×pow1 div-exp
2×cbrt-undiv expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×acos-asin rec-exp pow-flip 1-exp div-sub associate-/r/ distribute-neg-frac inv-pow
Counts
2 → 172
Calls
2 calls:
2.0ms
(/ (acos a) a)
11.0ms
(/ 1 (- (/ (acos a) a)))

series61.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (acos a) a)
26.0ms
(/ 1 (- (/ (acos a) a)))

simplify3.6s

Counts
178 → 178
Iterations

Useful iterations: 3 (614.0ms)

IterNodesCost
02652409
14872004
27891861
317191711
434571711
done50001711

prune225.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
930×times-frac
437×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
182×distribute-lft-neg-in distribute-rgt-neg-in
61×div-inv
33×associate-/r*
16×associate-/l*
15×add-exp-log
14×neg-mul-1
9×add-cbrt-cube
8×div-exp
4×cbrt-undiv
3×pow1
2×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
1×pow-flip associate-/r/ associate-/l/ distribute-neg-frac inv-pow
Counts
2 → 486
Calls
2 calls:
2.0ms
(/ 1 (acos a))
20.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

series30.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ 1 (acos a))
25.0ms
(/ (/ 1 (acos a)) (- (/ 1 a)))

simplify1.8s

Counts
492 → 492
Iterations

Useful iterations: done (1.8s)

IterNodesCost
071310319
118327603
230036678
done50006660

prune371.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (/ 1 (acos a)))
0.0b
(/ 1 (acos a))
0.4b
(/ (expm1 (log1p (/ 1 (acos a)))) (- (/ 1 a)))
1.0b
(expm1 (log1p (/ 1 (acos a))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
171×times-frac
103×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
52×distribute-lft-neg-in distribute-rgt-neg-in
33×associate-/r*
10×add-exp-log div-inv
8×add-cbrt-cube
6×associate-/l*
5×pow1 expm1-log1p-u
4×neg-mul-1 log1p-expm1-u add-log-exp
3×div-exp
2×cbrt-undiv frac-2neg clear-num expm1-udef
1×rec-exp log1p-udef expm1-log1p pow-flip 1-exp div-sub log1p-expm1 associate-/r/ distribute-neg-frac inv-pow
Counts
4 → 194
Calls
4 calls:
0.0ms
(log1p (/ 1 (acos a)))
2.0ms
(/ 1 (acos a))
10.0ms
(/ (expm1 (log1p (/ 1 (acos a)))) (- (/ 1 a)))
0.0ms
(expm1 (log1p (/ 1 (acos a))))

series401.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(log1p (/ 1 (acos a)))
5.0ms
(/ 1 (acos a))
188.0ms
(/ (expm1 (log1p (/ 1 (acos a)))) (- (/ 1 a)))
126.0ms
(expm1 (log1p (/ 1 (acos a))))

simplify2.3s

Counts
206 → 206
Iterations

Useful iterations: 3 (1.7s)

IterNodesCost
03013550
15342504
210852381
336672226
done50002226

prune291.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
045
done45

end0.0ms

sample487.0ms

Algorithm
intervals
Results
181.0ms8000×body80valid
117.0ms8067×body80nan