Details

Time bar (total: 9.8s)

sample34.0ms

Algorithm
intervals
Results
14.0ms267×body80valid
4.0ms87×body80nan

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13638
26637
312137
414937
516137
616237
done16237

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×prod-diff sqrt-prod
8×add-log-exp
7×fma-neg
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
1×distribute-lft-out--
Counts
4 → 91
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
23.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
103 → 103
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01302001
12901668
28841450
336481362
done50011361

prune350.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize118.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.5b
(/ (* a c) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
32×add-sqr-sqrt
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
9×times-frac associate-/r*
6×fma-neg add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 112
Calls
4 calls:
23.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
178.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify740.0ms

Counts
124 → 124
Iterations

Useful iterations: done (736.0ms)

IterNodesCost
02122318
15102017
219111714
done50001696

prune402.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize120.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
3.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
46×*-un-lft-identity
36×add-cube-cbrt
34×times-frac
30×add-exp-log
23×add-cbrt-cube
22×associate-*r*
18×prod-diff
16×sqrt-prod
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×fma-neg associate-/r* add-log-exp unswap-sqr
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 150
Calls
4 calls:
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
28.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
200.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
50.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
162 → 162
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02963451
18063097
231562275
done50002244

prune616.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize124.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
28×times-frac
25×add-exp-log
22×associate-*r*
21×add-cube-cbrt *-un-lft-identity
18×add-cbrt-cube
11×cbrt-prod
8×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp associate-*l*
6×sqrt-prod unswap-sqr
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip-- div-inv
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 105
Calls
4 calls:
25.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
140.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))

series285.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms
(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))

simplify798.0ms

Counts
117 → 117
Iterations

Useful iterations: done (794.0ms)

IterNodesCost
01952006
15491729
221581451
done50011445

prune607.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

regimes217.0ms

Accuracy

93.9% (1.0b remaining)

Error of 6.7b against oracle of 5.8b and baseline of 21.5b

bsearch149.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
2.028095266961813e+109
6
-2.0136180636941443e+142
-1.4127342237564056e+141
-2.7031326112465227e+141

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
049148
156148
done56148

end0.0ms

sample843.0ms

Algorithm
intervals
Results
445.0ms8700×body80valid
137.0ms2997×body80nan