Details

Time bar (total: 8.9s)

sample27.0ms

Algorithm
intervals
Results
10.0ms271×body80valid

simplify141.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0248
1438
2758
31208
41568
51898
62658
74518
810238
936328
1050018
done50018

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- t a))
0.0b
(* z (- b y))
0.5b
(+ (* x y) (* z (- t a)))
25.5b
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
56×*-un-lft-identity
54×prod-diff
52×add-cube-cbrt
33×distribute-rgt-in distribute-lft-in
22×associate-+r+
10×add-exp-log associate-*r* add-cbrt-cube
9×times-frac
8×pow1
6×sub-neg associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×flip3-+ associate-/r* flip-+ associate-/l*
2×flip3-- pow-prod-down prod-exp associate-/r/ *-commutative flip-- cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares unswap-sqr
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
4 → 161
Calls
4 calls:
25.0ms
(* z (- t a))
21.0ms
(* z (- b y))
12.0ms
(+ (* x y) (* z (- t a)))
35.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* z (- t a))
39.0ms
(* z (- b y))
52.0ms
(+ (* x y) (* z (- t a)))
379.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify90.0ms

Counts
173 → 173
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06231398
125361029
250021026
done50021026

prune464.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* z (- b y))
0.5b
(+ (* x y) (* z (- t a)))
0.6b
(/ 1 (+ y (* z (- b y))))
25.2b
(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
49×*-un-lft-identity
46×add-cube-cbrt
36×prod-diff
22×distribute-rgt-in associate-+r+ distribute-lft-in
20×times-frac associate-*r*
19×add-exp-log
13×add-cbrt-cube
9×pow1
6×associate-*l* add-log-exp
5×flip3-+ prod-exp flip-+
4×expm1-log1p-u sub-neg div-exp associate-/r/ log1p-expm1-u unswap-sqr
3×associate-*r/ associate-/r* cbrt-unprod associate-/l*
2×cbrt-undiv frac-times rec-exp 1-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative flip3-- pow-flip fma-def frac-2neg clear-num sum-log un-div-inv flip-- distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 161
Calls
4 calls:
23.0ms
(* z (- b y))
16.0ms
(+ (* x y) (* z (- t a)))
10.0ms
(/ 1 (+ y (* z (- b y))))
40.0ms
(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series565.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* z (- b y))
53.0ms
(+ (* x y) (* z (- t a)))
94.0ms
(/ 1 (+ y (* z (- b y))))
379.0ms
(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify95.0ms

Counts
173 → 173
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06581375
128301048
250011011
done50011011

prune492.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt b)
0.6b
(cbrt b)
0.6b
(cbrt b)
25.5b
(/ (+ (* x y) (* z (- t a))) (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
16×add-sqr-sqrt add-cube-cbrt
12×times-frac
9×cbrt-prod
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u distribute-lft-out add-log-exp
3×pow1/3 associate-/l*
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 76
Calls
4 calls:
1.0ms
(cbrt b)
1.0ms
(cbrt b)
1.0ms
(cbrt b)
55.0ms
(/ (+ (* x y) (* z (- t a))) (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))

series2.1s

Counts
4 → 12
Calls
4 calls:
190.0ms
(cbrt b)
195.0ms
(cbrt b)
192.0ms
(cbrt b)
1.5s
(/ (+ (* x y) (* z (- t a))) (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))

simplify45.0ms

Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02731127
111421032
250011009
done50011009

prune443.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.5b

localize32.0ms

Local error

Found 4 expressions with local error:

15.5b
(cbrt (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))
21.7b
(cbrt (+ (* x y) (* z (- t a))))
21.7b
(cbrt (+ (* x y) (* z (- t a))))
21.7b
(cbrt (+ (* x y) (* z (- t a))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
13×cbrt-prod
10×*-un-lft-identity
8×add-sqr-sqrt add-cube-cbrt cbrt-div
4×pow1 add-exp-log expm1-log1p-u flip3-+ pow1/3 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
1×distribute-lft-out
Counts
4 → 61
Calls
4 calls:
11.0ms
(cbrt (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))
8.0ms
(cbrt (+ (* x y) (* z (- t a))))
4.0ms
(cbrt (+ (* x y) (* z (- t a))))
5.0ms
(cbrt (+ (* x y) (* z (- t a))))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(cbrt (+ y (+ (* z (fma (* (cbrt b) (cbrt b)) (cbrt b) (- (* y 1)))) (* z (fma (- y) 1 y)))))
177.0ms
(cbrt (+ (* x y) (* z (- t a))))
177.0ms
(cbrt (+ (* x y) (* z (- t a))))
171.0ms
(cbrt (+ (* x y) (* z (- t a))))

simplify48.0ms

Counts
73 → 73
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0376988
11311920
25001887
done5001887

prune504.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.5b

regimes519.0ms

Accuracy

50.3% (5.2b remaining)

Error of 18.2b against oracle of 13.0b and baseline of 23.4b

bsearch102.0ms

Steps
ItersRangePoint
8
2.3069922374741435e+70
5.645474500853968e+74
1.8025388190473185e+72
10
-8.016544794788831e+91
-2.210389803822427e+75
-2.081581403037953e+85

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03914
13914
done3914

end0.0ms

sample712.0ms

Algorithm
intervals
Results
319.0ms8449×body80valid