Details

Time bar (total: 23.9s)

sample410.0ms

Algorithm
intervals
Results
102.0ms123×body320valid
54.0ms82×body160valid
32.0ms234×body80nan
32.0ms490×pre80true
11.0ms20×body640valid
5.0ms31×body80valid

simplify148.0ms

Counts
1 → 1
Iterations
IterNodes
done105
7105
6104
5102
494
377
244
125
014

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 53.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma b b (* (* a -4) c))
0.0b
(sqrt (fma b b (* (* a -4) c)))
0.1b
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
25.1b
(- (sqrt (fma b b (* (* a -4) c))) b)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
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 fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
0.0ms
(fma b b (* (* a -4) c))
2.0ms
(sqrt (fma b b (* (* a -4) c)))
34.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
18.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

series716.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma b b (* (* a -4) c))
86.0ms
(sqrt (fma b b (* (* a -4) c)))
140.0ms
(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
430.0ms
(- (sqrt (fma b b (* (* a -4) c))) b)

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
done2000
32000
21008
1423
0180

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.3b

localize18.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations
IterNodes
done0
00

prune79.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.3b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite40.0ms

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:
18.0ms
(/ (* a c) b)
21.0ms
(/ (* -2 (/ (* a c) b)) a)

series64.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (* a c) b)
36.0ms
(/ (* -2 (/ (* a c) b)) a)

simplify1.1s

Counts
59 → 59
Iterations
IterNodes
done2014
32014
21285
1282
0103

prune542.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 2.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ -2 (/ b (* c a)))
0.4b
(* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a))
0.5b
(* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a))
0.7b
(cbrt (* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a)))

rewrite541.0ms

Algorithm
rewrite-expression-head
Rules
1308×add-cbrt-cube add-exp-log
894×times-frac
779×cbrt-undiv div-exp
407×add-sqr-sqrt
367×prod-exp cbrt-unprod
365×*-un-lft-identity add-cube-cbrt
164×associate-*r*
83×associate-*l*
82×swap-sqr
70×div-inv
30×pow1
16×associate-/r/
12×unswap-sqr
11×frac-times associate-*l/
7×cbrt-div associate-/r* pow-plus associate-*r/ pow-prod-up
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×pow2 pow-sqr associate-/l*
2×pow3 *-commutative
1×cbrt-prod clear-num frac-2neg pow1/3 rem-cbrt-cube
Counts
4 → 770
Calls
4 calls:
18.0ms
(/ -2 (/ b (* c a)))
193.0ms
(* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a))
107.0ms
(* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a))
155.0ms
(cbrt (* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a)))

series256.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ -2 (/ b (* c a)))
61.0ms
(* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a))
36.0ms
(* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a))
108.0ms
(cbrt (* (* (/ (/ -2 (/ b (* c a))) a) (/ (/ -2 (/ b (* c a))) a)) (/ (/ -2 (/ b (* c a))) a)))

simplify1.7s

Counts
782 → 782
Iterations
IterNodes
done2000
12000
01059

prune9.0s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 2.3b

regimes566.0ms

Accuracy

0% (3.6b remaining)

Error of 6.3b against oracle of 2.7b and baseline of 6.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done8
18
07

end0.0ms

sample6.1s

Algorithm
intervals
Results
1.8s3644×body320valid
1.5s16149×pre80true
1.1s8149×body80nan
853.0ms2909×body160valid
266.0ms524×body640valid
117.0ms923×body80valid