Details

Time bar (total: 17.7s)

sample100.0ms

Algorithm
intervals
Results
17.0ms186×body80valid
16.0ms29×body2560valid
11.0ms24×body1280valid
10.0ms102×body80nan
5.0ms14×body640valid
4.0ms5×body5120valid
2.0ms9×body320valid
1.0ms4×body160valid

simplify104.0ms

Counts
1 → 1
Iterations
IterNodes
done120
5120
4112
383
242
122
012

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* 3.0 a) (- c) (* b b))
0.3b
(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
1.3b
(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
22.9b
(sqrt (fma (* 3.0 a) (- c) (* b b)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma (* 3.0 a) (- c) (* b b))
35.0ms
(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
14.0ms
(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
1.0ms
(sqrt (fma (* 3.0 a) (- c) (* b b)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(fma (* 3.0 a) (- c) (* b b))
195.0ms
(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
127.0ms
(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)
120.0ms
(sqrt (fma (* 3.0 a) (- c) (* b b)))

simplify778.0ms

Counts
110 → 110
Iterations
IterNodes
done5001
21258
1342
0148

prune563.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.1b

localize459.0ms

Local error

Found 4 expressions with local error:

2.0b
(+ b (sqrt (fma b b (* (- 3.0) (* c a)))))
3.5b
(/ (/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a)))))) (* 3.0 a))
10.8b
(/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a))))))
22.9b
(sqrt (fma b b (* (- 3.0) (* c a))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
53×*-un-lft-identity
32×add-sqr-sqrt
31×add-cube-cbrt
21×associate-/l*
18×add-cbrt-cube add-exp-log
11×distribute-lft-out
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 associate-/r*
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv
3×fma-def sqrt-prod
2×clear-num frac-2neg prod-exp cbrt-unprod
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 125
Calls
4 calls:
6.0ms
(+ b (sqrt (fma b b (* (- 3.0) (* c a)))))
26.0ms
(/ (/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a)))))) (* 3.0 a))
21.0ms
(/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a))))))
3.0ms
(sqrt (fma b b (* (- 3.0) (* c a))))

series819.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(+ b (sqrt (fma b b (* (- 3.0) (* c a)))))
286.0ms
(/ (/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a)))))) (* 3.0 a))
294.0ms
(/ (fma (* c a) (- 3.0) 0) (+ b (sqrt (fma b b (* (- 3.0) (* c a))))))
119.0ms
(sqrt (fma b b (* (- 3.0) (* c a))))

simplify1.2s

Counts
137 → 137
Iterations
IterNodes
done5002
22307
1519
0212

prune976.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b
(fma (* a c) (- 3.0) (* b b))
2.0b
(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
15.8b
(/ (* a c) a)
22.9b
(sqrt (fma (* a c) (- 3.0) (* b b)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt add-cbrt-cube add-exp-log
8×add-cube-cbrt
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* fma-def times-frac sqrt-prod
2×cbrt-undiv div-exp
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ pow1/2 prod-exp cbrt-unprod flip-+ fma-udef div-inv distribute-lft-out associate-/l*
Counts
4 → 65
Calls
4 calls:
0.0ms
(fma (* a c) (- 3.0) (* b b))
10.0ms
(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
14.0ms
(/ (* a c) a)
3.0ms
(sqrt (fma (* a c) (- 3.0) (* b b)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(fma (* a c) (- 3.0) (* b b))
136.0ms
(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
7.0ms
(/ (* a c) a)
147.0ms
(sqrt (fma (* a c) (- 3.0) (* b b)))

simplify646.0ms

Counts
77 → 77
Iterations
IterNodes
done5000
21330
1267
0111

prune639.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 3.0) (* (/ (- 3.0) (+ b (sqrt (fma (* a c) (- 3.0) (* b b))))) c))
0.7b
(fma (* a c) (- 3.0) (* b b))
2.0b
(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
22.9b
(sqrt (fma (* a c) (- 3.0) (* b b)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
25×add-cbrt-cube
20×prod-exp
15×*-un-lft-identity
14×add-sqr-sqrt
13×associate-*l* add-cube-cbrt
10×pow1 div-exp cbrt-unprod
9×times-frac
6×add-log-exp
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp fma-def 1-exp pow-prod-down associate-*l/ sqrt-prod
1×distribute-lft-neg-out frac-times +-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*r/ distribute-frac-neg *-commutative distribute-rgt-neg-out flip-+ fma-udef div-inv distribute-lft-out
Counts
4 → 90
Calls
4 calls:
92.0ms
(* (/ 1 3.0) (* (/ (- 3.0) (+ b (sqrt (fma (* a c) (- 3.0) (* b b))))) c))
1.0ms
(fma (* a c) (- 3.0) (* b b))
7.0ms
(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
1.0ms
(sqrt (fma (* a c) (- 3.0) (* b b)))

series529.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(* (/ 1 3.0) (* (/ (- 3.0) (+ b (sqrt (fma (* a c) (- 3.0) (* b b))))) c))
86.0ms
(fma (* a c) (- 3.0) (* b b))
130.0ms
(+ b (sqrt (fma (* a c) (- 3.0) (* b b))))
135.0ms
(sqrt (fma (* a c) (- 3.0) (* b b)))

simplify1.7s

Counts
102 → 102
Iterations
IterNodes
done5000
22747
1526
0182

prune507.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

regimes628.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.9b

bsearch278.0ms

Steps
ItersRangePoint
7
1.9371672431899034e+133
5.16149553175908e+134
6.945505805945457e+133
8
-3.651460945740179e-298
-7.119429034068498e-301
-3.203298721012043e-299
8
-9.061058506829192e+105
-7.154008779742083e+102
-5.062954969806706e+105

simplify3.2s

Iterations
IterNodes
done5001
144295
132239
121207
11687
10423
9287
8215
7175
6148
5115
497
393
284
163
043

end0.0ms

sample3.3s

Algorithm
intervals
Results
743.0ms2946×body80nan
675.0ms5958×body80valid
554.0ms1053×body2560valid
409.0ms880×body1280valid
183.0ms451×body640valid
109.0ms97×body5120valid
44.0ms216×body320valid
17.0ms113×body160valid