Details

Time bar (total: 23.9s)

sample103.0ms

Algorithm
intervals
Results
40.0ms823×body80nan
11.0ms196×body80valid
6.0ms9×body1280valid
6.0ms19×body640valid
4.0ms20×body320valid
1.0ms13×body160valid

simplify10.8s

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01417
12716
25616
310216
424016
558016
6133816
7307816
8449516
9475216
10482716
done482716

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b
(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
5.2b
(log (- 1.0 y))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
5×log-prod add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u fma-neg add-cbrt-cube log1p-expm1-u
2×log-div flip3-- flip-- fma-udef distribute-lft-out-- difference-of-squares
1×sub-neg diff-log rem-log-exp associate--l+ log-pow
Counts
3 → 57
Calls
3 calls:
3.0ms
(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
3.0ms
(log (- 1.0 y))

series306.0ms

Counts
3 → 9
Calls
3 calls:
147.0ms
(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
113.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
46.0ms
(log (- 1.0 y))

simplify2.3s

Counts
66 → 66
Iterations

Useful iterations: 3 (439.0ms)

IterNodesCost
01591368
13671221
210741068
34490953
done5000953

prune226.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b
(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×*-un-lft-identity
24×prod-diff
20×add-cube-cbrt
17×distribute-rgt-in distribute-lft-in
11×pow1
7×log-pow
6×log-prod flip3-- associate-*r* associate--l+ flip--
5×associate-*l*
4×add-exp-log frac-times add-cbrt-cube
3×distribute-lft-out--
2×expm1-log1p-u sub-neg associate-*r/ associate-*l/ log1p-expm1-u add-log-exp difference-of-squares
1×pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
2 → 77
Calls
2 calls:
25.0ms
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series178.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
110.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify684.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (139.0ms)

IterNodesCost
01884010
14052951
217672397
done50002397

prune290.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.7b
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.7b
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.7b
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
58×cbrt-prod
52×*-un-lft-identity
37×add-sqr-sqrt
22×pow1 distribute-lft-out--
18×cbrt-div
15×add-cube-cbrt swap-sqr
11×log-pow
9×flip3-- pow1/3 associate-*r* associate-*l* flip--
7×difference-of-squares
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 119
Calls
4 calls:
25.0ms
(* (cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
3.0ms
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
5.0ms
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
3.0ms
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

series908.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(* (cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
222.0ms
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
214.0ms
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
218.0ms
(cbrt (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

simplify585.0ms

Counts
131 → 131
Iterations

Useful iterations: 2 (168.0ms)

IterNodesCost
02175308
15174954
218274691
done50014691

prune653.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (- x 1.0) (log y) (* (- z 1.0) (+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))))
8.4b
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
11.9b
(log (- (sqrt 1.0) (sqrt y)))
12.0b
(log (+ (sqrt 1.0) (sqrt y)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
28×log-prod
25×add-sqr-sqrt
16×sqrt-prod
11×pow1
9×add-cube-cbrt associate-+r+
8×log-div distribute-lft-out difference-of-squares
7×log-pow
6×add-exp-log
5×associate-+l+
4×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u distribute-lft-out-- add-log-exp
3×flip3-+ flip-+
2×associate-+l- associate-+r- flip3-- rem-log-exp flip--
1×+-commutative sum-log fma-udef
Counts
4 → 89
Calls
4 calls:
0.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))))
15.0ms
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
7.0ms
(log (- (sqrt 1.0) (sqrt y)))
5.0ms
(log (+ (sqrt 1.0) (sqrt y)))

series1.1s

Counts
4 → 12
Calls
4 calls:
477.0ms
(fma (- x 1.0) (log y) (* (- z 1.0) (+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))))
309.0ms
(+ (log (+ (sqrt 1.0) (sqrt y))) (log (- (sqrt 1.0) (sqrt y))))
150.0ms
(log (- (sqrt 1.0) (sqrt y)))
144.0ms
(log (+ (sqrt 1.0) (sqrt y)))

simplify1.8s

Counts
101 → 101
Iterations

Useful iterations: 3 (380.0ms)

IterNodesCost
01761803
14051647
211161270
343411232
done50001232

prune367.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes328.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02027
12227
done2227

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s24472×body80nan
319.0ms5804×body80valid
256.0ms833×body640valid
162.0ms265×body1280valid
130.0ms695×body320valid
50.0ms434×body160valid