Details

Time bar (total: 17.2s)

sample73.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
14.0ms222×body80nan

simplify37.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05017
110817
238917
3176117
4500217
done500217

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (sqrt (+ t a)))
0.5b
(/ 2.0 (* t 3.0))
3.4b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
4.0b
(/ (* z (sqrt (+ t a))) t)

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
63×prod-diff
62×associate--r+
49×add-sqr-sqrt
45×add-cube-cbrt
36×times-frac
31×distribute-rgt-in distribute-lft-in
20×frac-sub
16×add-exp-log add-cbrt-cube
15×distribute-lft-out
12×div-inv
9×flip3-- flip--
8×frac-times associate-*r/
7×fma-neg associate-*r*
6×pow1 add-log-exp
5×flip3-+ sqrt-prod flip-+
4×cbrt-undiv expm1-log1p-u sqrt-div div-exp associate-/r* log1p-expm1-u associate-/l*
3×sub-neg associate-*l* prod-exp cbrt-unprod
2×frac-2neg associate-*l/ associate--l+ clear-num associate-/l/ unswap-sqr
1×diff-log pow-prod-down *-commutative
Counts
4 → 179
Calls
4 calls:
21.0ms
(* z (sqrt (+ t a)))
8.0ms
(/ 2.0 (* t 3.0))
63.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
17.0ms
(/ (* z (sqrt (+ t a))) t)

series353.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* z (sqrt (+ t a)))
16.0ms
(/ 2.0 (* t 3.0))
188.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
83.0ms
(/ (* z (sqrt (+ t a))) t)

simplify49.0ms

Counts
191 → 191
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013772637
150012324
done50012324

prune913.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
0.3b
(/ (sqrt (+ t a)) t)
0.5b
(/ 2.0 (* t 3.0))
2.7b
(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
97×*-un-lft-identity
60×add-sqr-sqrt
56×prod-diff
54×add-cube-cbrt
48×times-frac
31×distribute-rgt-in distribute-lft-in
19×distribute-lft-out
16×sqrt-prod
13×add-exp-log add-cbrt-cube
10×div-inv associate-/l*
8×frac-times flip3-- flip--
6×pow1 associate-*r* frac-sub
5×associate-*l*
4×expm1-log1p-u flip3-+ associate-*r/ associate-/r* flip-+ log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp distribute-lft-out--
2×sub-neg frac-2neg sqrt-div associate-*l/ prod-exp associate--l+ clear-num cbrt-unprod associate-/l/ difference-of-squares
1×pow-prod-down *-commutative fma-udef unswap-sqr
Counts
4 → 181
Calls
4 calls:
209.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
15.0ms
(/ (sqrt (+ t a)) t)
11.0ms
(/ 2.0 (* t 3.0))
0.0ms
(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

series360.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
63.0ms
(/ (sqrt (+ t a)) t)
16.0ms
(/ 2.0 (* t 3.0))
221.0ms
(fma (/ z 1) (/ (sqrt (+ t a)) t) (- (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))

simplify106.0ms

Counts
193 → 193
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
08942691
140232163
250022158
done50022158

prune743.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 2.0 (* t 3.0))
3.4b
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (pow (/ 2.0 (* t 3.0)) 3)))))
4.0b
(/ (* z (sqrt (+ t a))) t)
38.8b
(cbrt (pow (/ 2.0 (* t 3.0)) 3))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
203×*-un-lft-identity
191×prod-diff
190×associate--r+
180×cbrt-prod
111×add-sqr-sqrt add-cube-cbrt
95×distribute-rgt-in distribute-lft-in
66×times-frac
63×unpow-prod-down cube-prod
46×distribute-lft-out
22×div-inv
20×frac-sub
14×add-exp-log add-cbrt-cube
9×cube-mult flip3-- unpow3 flip-- sqr-pow
8×frac-times
7×cube-div cbrt-div fma-neg
6×associate-*r/ add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u flip3-+ div-exp associate-/r* flip-+ log1p-expm1-u associate-/l*
3×sub-neg
2×frac-2neg sqrt-div associate-*l/ prod-exp associate--l+ clear-num cbrt-unprod associate-/l/
1×pow1/3 diff-log rem-cbrt-cube
Counts
4 → 312
Calls
4 calls:
7.0ms
(/ 2.0 (* t 3.0))
94.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (pow (/ 2.0 (* t 3.0)) 3)))))
14.0ms
(/ (* z (sqrt (+ t a))) t)
6.0ms
(cbrt (pow (/ 2.0 (* t 3.0)) 3))

series313.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ 2.0 (* t 3.0))
192.0ms
(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (cbrt (pow (/ 2.0 (* t 3.0)) 3)))))
75.0ms
(/ (* z (sqrt (+ t a))) t)
25.0ms
(cbrt (pow (/ 2.0 (* t 3.0)) 3))

simplify75.0ms

Counts
324 → 324
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
016835517
150014999
done50014999

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

3.1b
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
3.9b
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
4.9b
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
25.2b
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
766×associate-*l/
764×associate-*r/
524×frac-sub
498×flip3-- flip--
364×frac-times
240×sqrt-div
162×associate-/l/
120×flip3-+ flip-+
28×add-exp-log add-cbrt-cube
24×distribute-rgt-in distribute-lft-in
14×pow1
12×prod-exp cbrt-unprod associate--r+
9×sub-neg prod-diff
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*l*
6×pow-prod-down add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×times-frac associate-/l*
2×associate-*r* associate-/r/ *-commutative
1×frac-2neg fma-neg diff-log div-sub clear-num associate-/r* div-inv difference-of-squares
Counts
4 → 455
Calls
4 calls:
36.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
292.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
448.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
653.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0))
187.0ms
(* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))
598.0ms
(- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0)))))
944.0ms
(/ (- (* (* z (sqrt (+ t a))) (* (- a (/ 5.0 6.0)) (* t 3.0))) (* t (* (- b c) (- (* (- (* a a) (* (/ 5.0 6.0) (/ 5.0 6.0))) (* t 3.0)) (* (- a (/ 5.0 6.0)) 2.0))))) (* t (* (- a (/ 5.0 6.0)) (* t 3.0))))

simplify284.0ms

Counts
467 → 467
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0490623936
1500123936
done500123936

prune6.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes280.0ms

Accuracy

1.8% (1.7b remaining)

Error of 2.2b against oracle of 0.6b and baseline of 2.3b

bsearch321.0ms

Steps
ItersRangePoint
8
4.1010416576246345e-198
1.9400159718978306e-193
1.296544899920866e-195
8
-3.946899936095388e-217
-6.176372438192837e-220
-1.0295064487473734e-217

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08352
18752
28752
done8752

end0.0ms

sample2.0s

Algorithm
intervals
Results
557.0ms8000×body80valid
509.0ms8029×body80nan