Details

Time bar (total: 15.2s)

sample32.0ms

Algorithm
intervals
Results
15.0ms490×body80valid

simplify6.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (42.0ms)

IterNodesCost
01113
12113
25113
315013
434712
566612
694412
7115012
8144812
9172612
10178912
done178912

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* z z) t)
3.6b
(* (* y 4.0) (- (* z z) t))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×prod-diff
8×add-sqr-sqrt
7×pow1 add-exp-log add-cbrt-cube
6×add-cube-cbrt *-un-lft-identity
5×distribute-rgt-in distribute-lft-in
4×associate-*r* add-log-exp
3×sub-neg pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u difference-of-squares
1×fma-neg diff-log associate-*l* *-commutative
Counts
2 → 52
Calls
2 calls:
4.0ms
(- (* z z) t)
14.0ms
(* (* y 4.0) (- (* z z) t))

series86.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- (* z z) t)
64.0ms
(* (* y 4.0) (- (* z z) t))

simplify610.0ms

Counts
58 → 58
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
0108760
1299662
21265544
done5000544

prune131.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize14.0ms

Local error

Found 4 expressions with local error:

3.6b
(* (* y 4.0) (- (* z z) t))
5.3b
(cbrt (* (* y 4.0) (- (* z z) t)))
5.3b
(cbrt (* (* y 4.0) (- (* z z) t)))
5.3b
(cbrt (* (* y 4.0) (- (* z z) t)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt associate-*r/
7×add-cube-cbrt *-un-lft-identity
6×cbrt-div prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u flip3-- associate-*r* flip-- log1p-expm1-u add-log-exp
3×cbrt-prod pow1/3 pow-prod-down prod-exp cbrt-unprod
2×sub-neg
1×associate-*l* *-commutative difference-of-squares
Counts
4 → 72
Calls
4 calls:
14.0ms
(* (* y 4.0) (- (* z z) t))
8.0ms
(cbrt (* (* y 4.0) (- (* z z) t)))
8.0ms
(cbrt (* (* y 4.0) (- (* z z) t)))
8.0ms
(cbrt (* (* y 4.0) (- (* z z) t)))

series516.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* y 4.0) (- (* z z) t))
150.0ms
(cbrt (* (* y 4.0) (- (* z z) t)))
143.0ms
(cbrt (* (* y 4.0) (- (* z z) t)))
154.0ms
(cbrt (* (* y 4.0) (- (* z z) t)))

simplify642.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
01441279
13741185
214261011
done50011011

prune303.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* z z) t)
1.1b
(- (pow z 4) (* t t))
10.2b
(* (* y 4.0) (- (pow z 4) (* t t)))
20.2b
(/ (* (* y 4.0) (- (pow z 4) (* t t))) (+ (* z z) t))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
21×prod-diff
19×add-sqr-sqrt
18×add-exp-log add-cbrt-cube
15×add-cube-cbrt *-un-lft-identity
14×unpow-prod-down
9×pow1 distribute-rgt-in distribute-lft-in
8×add-log-exp
7×fma-neg
6×associate-*r* prod-exp cbrt-unprod difference-of-squares sqr-pow
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×cbrt-undiv sub-neg flip3-- times-frac div-exp pow-prod-down associate-/r* flip--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×+-commutative fma-def frac-2neg diff-log associate-*l* clear-num sum-log *-commutative div-inv associate-/l*
Counts
4 → 117
Calls
4 calls:
3.0ms
(+ (* z z) t)
8.0ms
(- (pow z 4) (* t t))
21.0ms
(* (* y 4.0) (- (pow z 4) (* t t)))
26.0ms
(/ (* (* y 4.0) (- (pow z 4) (* t t))) (+ (* z z) t))

series344.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(+ (* z z) t)
42.0ms
(- (pow z 4) (* t t))
114.0ms
(* (* y 4.0) (- (pow z 4) (* t t)))
160.0ms
(/ (* (* y 4.0) (- (pow z 4) (* t t))) (+ (* z z) t))

simplify1.3s

Counts
129 → 129
Iterations

Useful iterations: 2 (201.0ms)

IterNodesCost
01882146
15591995
227801670
done50001670

prune401.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (/ (fma z z t) (* (* 4.0 y) (- (pow z 4) (* t t)))))
1.1b
(- (pow z 4) (* t t))
10.2b
(* (* 4.0 y) (- (pow z 4) (* t t)))
20.1b
(/ (fma z z t) (* (* 4.0 y) (- (pow z 4) (* t t))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log
42×times-frac
37×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
32×add-cbrt-cube
21×prod-diff
20×div-exp
15×prod-exp
14×unpow-prod-down
12×associate-*r/
11×associate-/r/
10×pow1 cbrt-undiv associate-/r*
9×distribute-rgt-in distribute-lft-in cbrt-unprod
7×flip3-- fma-neg flip--
6×associate-*r* div-inv associate-/l* add-log-exp difference-of-squares sqr-pow
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
3×sub-neg pow-prod-down
2×frac-2neg clear-num
1×pow-flip diff-log associate-*l* *-commutative inv-pow
Counts
4 → 171
Calls
4 calls:
26.0ms
(/ 1 (/ (fma z z t) (* (* 4.0 y) (- (pow z 4) (* t t)))))
9.0ms
(- (pow z 4) (* t t))
21.0ms
(* (* 4.0 y) (- (pow z 4) (* t t)))
11.0ms
(/ (fma z z t) (* (* 4.0 y) (- (pow z 4) (* t t))))

series355.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ 1 (/ (fma z z t) (* (* 4.0 y) (- (pow z 4) (* t t)))))
44.0ms
(- (pow z 4) (* t t))
119.0ms
(* (* 4.0 y) (- (pow z 4) (* t t)))
82.0ms
(/ (fma z z t) (* (* 4.0 y) (- (pow z 4) (* t t))))

simplify2.4s

Counts
183 → 183
Iterations

Useful iterations: 2 (296.0ms)

IterNodesCost
02563853
16723609
232962991
done50002991

prune474.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.5b

regimes301.0ms

Accuracy

82.9% (0.5b remaining)

Error of 3.3b against oracle of 2.8b and baseline of 5.8b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02036
12536
done2536

end0.0ms

sample921.0ms

Algorithm
intervals
Results
509.0ms15703×body80valid