Details

Time bar (total: 15.2s)

sample182.0ms

Algorithm
intervals
Results
66.0ms299×body80nan
37.0ms156×body160valid
29.0ms555×pre80true
18.0ms49×body320valid
7.0ms51×body80valid

simplify109.0ms

Counts
1 → 1
Iterations
IterNodes
8105
7105
6104
5102
494
377
244
125
014

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.3b

localize46.0ms

Local error

Found 3 expressions with local error:

0.1b
(sqrt (fma b b (* (* a -4) c)))
0.1b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
39.5b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
39×*-un-lft-identity
29×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×fma-neg associate-/l*
5×add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
4×pow1
3×expm1-log1p-u associate-/r* insert-posit16 log1p-expm1-u
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp div-inv
Counts
3 → 103
Calls
3 calls:
2.0ms
(sqrt (fma b b (* (* a -4) c)))
39.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
16.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series350.0ms

Counts
3 → 9
Calls
3 calls:
103.0ms
(sqrt (fma b b (* (* a -4) c)))
136.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
111.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.1s

Counts
112 → 112
Iterations
IterNodes
32301
2881
1389
0170

prune975.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
10
00

prune91.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.4b

localize31.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.3b
(/ (* -2 (/ (* a c) b)) a)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
21×add-cbrt-cube add-exp-log
8×cbrt-undiv div-exp
6×add-sqr-sqrt associate-/r* *-un-lft-identity times-frac add-cube-cbrt
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
1×associate-*r/ associate-/l/
Counts
2 → 53
Calls
2 calls:
13.0ms
(/ (* a c) b)
17.0ms
(/ (* -2 (/ (* a c) b)) a)

series60.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (* a c) b)
31.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify2.5s

Counts
59 → 59
Iterations
IterNodes
36399
21058
1267
0103

prune452.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (/ (* a c) b))
0.2b
(/ (* a c) b)
0.3b
(/ (* -2 (expm1 (log1p (/ (* a c) b)))) a)
0.3b
(expm1 (log1p (/ (* a c) b)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/r* times-frac
5×expm1-log1p-u
4×pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg prod-exp cbrt-unprod div-inv associate-/l*
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
4 → 72
Calls
4 calls:
1.0ms
(log1p (/ (* a c) b))
13.0ms
(/ (* a c) b)
9.0ms
(/ (* -2 (expm1 (log1p (/ (* a c) b)))) a)
0.0ms
(expm1 (log1p (/ (* a c) b)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(log1p (/ (* a c) b))
23.0ms
(/ (* a c) b)
116.0ms
(/ (* -2 (expm1 (log1p (/ (* a c) b)))) a)
142.0ms
(expm1 (log1p (/ (* a c) b)))

simplify2.5s

Counts
84 → 84
Iterations
IterNodes
34869
2987
1324
0144

prune637.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.4b

regimes634.0ms

Accuracy

9% (6.2b remaining)

Error of 11.2b against oracle of 5.0b and baseline of 11.8b

bsearch32.0ms

Steps
ItersRangePoint
2
0.11906653961437699
0.12902613394488163
0.12005985553413497

simplify7.0ms

Iterations
IterNodes
229
129
024

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.4s4836×body160valid
1.1s8328×body80nan
828.0ms16328×pre80true
571.0ms1384×body320valid
242.0ms1780×body80valid