Details

Time bar (total: 22.9s)

sample58.0ms

Algorithm
intervals
Results
26.0ms515×body80valid

simplify3.5s

Counts
1 → 1
Iterations

Useful iterations: 4 (98.0ms)

IterNodesCost
01113
12113
25213
317113
434612
558612
669812
780512
8104212
9122512
10122812
done122812

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.4b
(* (* y 4.0) (- (* z z) t))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
13×prod-diff
10×distribute-rgt-in distribute-lft-in associate--r+
8×add-sqr-sqrt
7×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×sub-neg
4×associate-*r* add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u
1×fma-neg diff-log associate-*l* *-commutative difference-of-squares
Counts
2 → 59
Calls
2 calls:
21.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
74.0ms
(* (* y 4.0) (- (* z z) t))

series200.0ms

Counts
2 → 6
Calls
2 calls:
102.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
98.0ms
(* (* y 4.0) (- (* z z) t))

simplify1.2s

Counts
65 → 65
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01361075
1364959
21221843
done5000815

prune232.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 4.0 (* y (- t (* z z))))
6.4b
(* y (- t (* z z)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
25×distribute-rgt-in distribute-lft-in
18×prod-diff
14×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×pow1 add-exp-log add-cbrt-cube
6×sub-neg associate-*r/ associate-*l*
5×associate-*r*
4×pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u flip3-- *-commutative flip-- log1p-expm1-u add-log-exp
1×difference-of-squares unswap-sqr
Counts
2 → 75
Calls
2 calls:
67.0ms
(* 4.0 (* y (- t (* z z))))
37.0ms
(* y (- t (* z z)))

series231.0ms

Counts
2 → 6
Calls
2 calls:
127.0ms
(* 4.0 (* y (- t (* z z))))
104.0ms
(* y (- t (* z z)))

simplify3.2s

Counts
81 → 81
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01221117
12821099
2830951
34169927
done5000927

prune269.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
2.5b
(* (cbrt y) (- t (* z z)))
4.3b
(* (* (cbrt y) (cbrt y)) (* (cbrt y) (- t (* z z))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
25×distribute-rgt-in distribute-lft-in
20×add-sqr-sqrt
18×pow1 add-exp-log prod-diff
15×add-cube-cbrt *-un-lft-identity
11×add-cbrt-cube
10×cbrt-prod
9×pow-prod-down prod-exp cbrt-unprod
7×associate-*l*
6×sub-neg associate-*r/
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×flip3-- pow1/3 *-commutative flip-- unswap-sqr
1×difference-of-squares
Counts
4 → 109
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
25.0ms
(* (cbrt y) (- t (* z z)))
103.0ms
(* (* (cbrt y) (cbrt y)) (* (cbrt y) (- t (* z z))))

series1.1s

Counts
4 → 12
Calls
4 calls:
305.0ms
(cbrt y)
310.0ms
(cbrt y)
350.0ms
(* (cbrt y) (- t (* z z)))
147.0ms
(* (* (cbrt y) (cbrt y)) (* (cbrt y) (- t (* z z))))

simplify1.7s

Counts
121 → 121
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01511780
13991739
213551278
done50001046

prune458.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma x x (* (* y t) 4.0))
0.0b
(* (* y t) 4.0)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×associate-*l* *-commutative fma-udef
Counts
2 → 30
Calls
2 calls:
0.0ms
(fma x x (* (* y t) 4.0))
19.0ms
(* (* y t) 4.0)

series115.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(fma x x (* (* y t) 4.0))
34.0ms
(* (* y t) 4.0)

simplify7.0s

Counts
36 → 36
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
057307
1121299
2447253
31648253
43918253
done5000253

prune119.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.2b

regimes578.0ms

Accuracy

78.9% (0.8b remaining)

Error of 3.3b against oracle of 2.5b and baseline of 6.2b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02034
12634
done2634

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.6s16035×body80valid