Details

Time bar (total: 15.9s)

sample97.0ms

Algorithm
intervals
Results
20.0ms204×body80valid
17.0ms36×body1280valid
14.0ms25×body2560valid
9.0ms104×body80nan
6.0ms15×body640valid
1.0ms5×body320valid
1.0ms1×body5120valid
1.0ms3×body160valid

simplify198.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12817
26417
311417
414117
515117
615517
done15517

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
105.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
32.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
119.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms
(- (* b b) (* 4.0 (* a c)))
113.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify926.0ms

Counts
89 → 89
Iterations

Useful iterations: done (921.0ms)

IterNodesCost
01571750
14181650
216411474
done50011466

prune415.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.1b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
3.7b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.2b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
77×add-sqr-sqrt
56×*-un-lft-identity
36×add-cube-cbrt
27×associate-/l*
20×difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 138
Calls
4 calls:
18.0ms
(- (* b b) (* 4.0 (* a c)))
168.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
102.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series844.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (* b b) (* 4.0 (* a c)))
257.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
381.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
117.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.8s

Counts
150 → 150
Iterations

Useful iterations: 2 (816.0ms)

IterNodesCost
02514460
16603964
240403668
done50013668

prune664.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/r*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
62.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
40.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series561.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
146.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms
(- (* b b) (* 4.0 (* a c)))
96.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
88 → 88
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01471693
13841585
217621417
done50001399

prune373.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
133.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
51.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series486.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
130.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
89.0ms
(- (* b b) (* 4.0 (* a c)))
95.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts
97 → 97
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01832003
14921837
224111573
done50011569

prune347.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 7.1b

regimes283.0ms

Accuracy

87.6% (3.5b remaining)

Error of 9.1b against oracle of 5.6b and baseline of 33.4b

bsearch332.0ms

Steps
ItersRangePoint
8
1.051086597250448e+104
1.8086281629461872e+108
1.7117942217659455e+108
10
-1.3504024217230283e-126
-3.821635312053031e-137
-1.0525520649644557e-131
8
-1.797023714648992e+49
-8.642842160642246e+45
-2.7739413630925597e+46

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
03869
14567
done4567

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.1s1039×body2560valid
721.0ms5893×body80valid
485.0ms480×body640valid
485.0ms929×body1280valid
227.0ms2950×body80nan
52.0ms229×body320valid
50.0ms87×body5120valid
18.0ms109×body160valid