Details

Time bar (total: 38.5s)

sample282.0ms

Algorithm
intervals
Results
108.0ms784×body80nan
25.0ms186×body80valid
18.0ms26×body640valid
16.0ms11×body1280valid
12.0ms25×body320valid
3.0ms11×body160valid

simplify6.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
01417
12716
25716
313516
438816
5130616
6367016
done500016

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- z 1.0) (log (- 1.0 y)))
0.0b
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b
(* (- x 1.0) (log y))
5.8b
(log (- 1.0 y))

rewrite305.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
32×*-un-lft-identity
21×log-prod
20×add-cube-cbrt
11×pow1
10×associate-*l*
9×add-exp-log prod-diff add-log-exp
8×distribute-rgt-in distribute-lft-in associate-*r* add-cbrt-cube
6×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u flip3-- associate-*l/ flip-- log1p-expm1-u
3×fma-neg log-pow
2×log-div diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-log-exp associate--l+ sum-log
Counts
4 → 114
Calls
4 calls:
57.0ms
(* (- z 1.0) (log (- 1.0 y)))
183.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
47.0ms
(* (- x 1.0) (log y))
11.0ms
(log (- 1.0 y))

series546.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (- z 1.0) (log (- 1.0 y)))
277.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
112.0ms
(* (- x 1.0) (log y))
84.0ms
(log (- 1.0 y))

simplify2.9s

Counts
126 → 126
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02632037
16321852
224871613
done50001518

prune966.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 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))))))
0.0b
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b
(* (- x 1.0) (log y))

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
60×*-un-lft-identity
57×prod-diff
51×add-cube-cbrt
40×distribute-rgt-in distribute-lft-in
34×associate-+r+
28×flip3-- flip--
24×log-prod associate-*l/
22×pow1
16×frac-add
14×log-pow
13×associate--l+
12×frac-times
11×add-log-exp
10×associate-*r* associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-+l+ associate-*r/
5×sub-neg distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×fma-neg
2×diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×+-commutative fma-def flip3-+ flip-+
Counts
4 → 198
Calls
4 calls:
80.0ms
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
179.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
51.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
49.0ms
(* (- x 1.0) (log y))

series1.0s

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
452.0ms
(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
339.0ms
(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
99.0ms
(* (- x 1.0) (log y))

simplify1.1s

Counts
210 → 210
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04159275
111727277
done50016576

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.1b
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.1b
(* (- x 1.0) (log y))
0.4b
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite521.0ms

Algorithm
rewrite-expression-head
Rules
192×sqrt-prod
168×prod-diff
133×add-sqr-sqrt
131×*-un-lft-identity
117×add-cube-cbrt
98×associate-*l/
95×distribute-rgt-in distribute-lft-in
88×frac-times associate-+r+
84×flip3-- flip--
52×frac-add
40×pow1
31×flip3-+ flip-+
27×log-pow
26×associate-*r/
20×associate-*r*
13×add-exp-log add-cbrt-cube
12×log-prod
11×associate-*l*
6×associate-+l+ add-log-exp difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod distribute-lft-out--
4×expm1-log1p-u sub-neg log1p-expm1-u
3×*-commutative distribute-lft-out
2×unswap-sqr
1×+-commutative fma-def sum-log
Counts
4 → 367
Calls
4 calls:
94.0ms
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
111.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
47.0ms
(* (- x 1.0) (log y))
222.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
253.0ms
(+ (* (- x 1.0) (log y)) (* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
265.0ms
(* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
102.0ms
(* (- x 1.0) (log y))
464.0ms
(* (* (- z 1.0) (+ (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify1.9s

Counts
379 → 379
Iterations

Useful iterations: done (1.9s)

IterNodesCost
068734860
1231826855
done500125845

prune4.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize98.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (cbrt y) (cbrt y))
0.7b
(cbrt y)
0.7b
(cbrt y)
0.7b
(cbrt y)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
21.0ms
(* (cbrt y) (cbrt y))
1.0ms
(cbrt y)
2.0ms
(cbrt y)
2.0ms
(cbrt y)

series1.6s

Counts
4 → 12
Calls
4 calls:
427.0ms
(* (cbrt y) (cbrt y))
391.0ms
(cbrt y)
379.0ms
(cbrt y)
370.0ms
(cbrt y)

simplify1.6s

Counts
93 → 93
Iterations

Useful iterations: done (1.6s)

IterNodesCost
065554
1143443
2719423
done5000409

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes996.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02740
13140
done3140

end0.0ms

sample9.1s

Algorithm
intervals
Results
4.5s23483×body80nan
930.0ms5871×body80valid
573.0ms747×body640valid
295.0ms252×body1280valid
292.0ms734×body320valid
110.0ms427×body160valid