Details

Time bar (total: 25.2s)

sample80.0ms

Algorithm
intervals
Results
16.0ms189×body80valid
8.0ms26×body640valid
7.0ms114×body80nan
7.0ms17×body1280valid
5.0ms19×body640nan
4.0ms10×body1280nan
4.0ms16×body320valid
2.0ms9×body320nan
1.0ms8×body160valid
0.0ms2×body160nan

simplify141.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22912
34112
45412
56212
67012
78512
810312
911612
done11612

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x y) (- 1.0 y))
2.9b
(- 1.0 (/ (- x y) (- 1.0 y)))
4.7b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
175×add-sqr-sqrt
169×*-un-lft-identity
102×times-frac
93×prod-diff
81×add-cube-cbrt
46×difference-of-squares
44×distribute-lft-out--
8×associate-/r/
7×flip3-- flip--
6×add-exp-log log-prod
5×associate-/r* add-cbrt-cube associate-/l* add-log-exp
4×pow1 div-inv
3×expm1-log1p-u fma-neg log1p-expm1-u
2×log-div div-sub associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp rem-log-exp clear-num log-pow associate--r-
Counts
3 → 187
Calls
3 calls:
26.0ms
(/ (- x y) (- 1.0 y))
45.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
63.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series241.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(/ (- x y) (- 1.0 y))
76.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
97.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.8s

Counts
196 → 196
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03347257
18396666
222924956
done50004113

prune505.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cbrt (- 1.0 y)) 3)
0.3b
(pow (cbrt (- 1.0 y)) 3)
4.7b
(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
10.4b
(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

rewrite7.6s

Algorithm
rewrite-expression-head
Rules
2731×add-sqr-sqrt
2645×*-un-lft-identity
2088×prod-diff
2016×times-frac
1648×cbrt-prod
1464×add-cube-cbrt unpow-prod-down cube-prod
622×difference-of-squares
584×distribute-lft-out--
222×sqr-pow
209×cube-mult unpow3
40×cube-div cbrt-div
36×associate-/r/
24×flip3-- flip--
18×fma-neg div-inv
10×distribute-lft-out
9×log-prod
8×log-div frac-add
7×pow1 add-exp-log
6×pow-unpow add-log-exp
4×expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u
3×flip3-+ flip-+
2×pow-to-exp distribute-rgt-neg-in pow1/3 pow-exp distribute-neg-frac rem-cube-cbrt
1×sub-neg diff-log div-sub rem-log-exp log-pow associate--r-
Counts
4 → 2268
Calls
4 calls:
10.0ms
(pow (cbrt (- 1.0 y)) 3)
17.0ms
(pow (cbrt (- 1.0 y)) 3)
6.8s
(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
322.0ms
(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

series1.0s

Counts
4 → 12
Calls
4 calls:
408.0ms
(pow (cbrt (- 1.0 y)) 3)
390.0ms
(pow (cbrt (- 1.0 y)) 3)
129.0ms
(log (+ (- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3))) (+ (/ (- x y) (pow (cbrt (- 1.0 y)) 3)) (- (/ (- x y) (pow (cbrt (- 1.0 y)) 3))))))
74.0ms
(- (pow (cbrt 1.0) 3) (/ (- x y) (pow (cbrt (- 1.0 y)) 3)))

simplify2.6s

Counts
2280 → 2280
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01304187609
12919133115
done500068623

prune917.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))))))
2.9b
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
12.4b
(log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))))))
13.8b
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
1120×add-sqr-sqrt
1014×*-un-lft-identity
832×prod-diff
633×unpow-prod-down cube-prod
624×times-frac
500×add-cube-cbrt
313×difference-of-squares
259×distribute-lft-out--
111×sqr-pow
81×cube-mult unpow3
72×log-prod
48×associate-/r/
33×associate--l+
28×flip3-- flip--
24×div-inv
19×pow1
16×fma-neg
15×log-pow
6×add-exp-log add-log-exp
4×expm1-log1p-u log-div add-cbrt-cube log1p-expm1-u
3×difference-cubes associate--r+
2×associate--l- sub-neg diff-log rem-log-exp
Counts
4 → 1009
Calls
4 calls:
169.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))))))
227.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
1.0ms
(log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))))))
578.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

series1.5s

Counts
4 → 12
Calls
4 calls:
522.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y)))))))
250.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
236.0ms
(log (fma 1.0 1.0 (* (/ (- x y) (- 1.0 y)) (+ 1.0 (/ (- x y) (- 1.0 y))))))
446.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))

simplify1.3s

Counts
1021 → 1021
Iterations

Useful iterations: done (1.2s)

IterNodesCost
073171293
1175458515
done500142997

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y))
3.8b
(fma (/ x (pow y 2)) 1.0 (/ x y))
4.1b
(log (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y)))
9.0b
(/ x (pow y 2))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
61×*-un-lft-identity
57×add-cube-cbrt
53×times-frac
39×prod-diff
12×unpow-prod-down
10×add-exp-log
8×associate-/r*
6×log-prod add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u div-inv unpow2 difference-of-squares sqr-pow
3×fma-neg div-exp associate-/l*
2×log-div flip3-- flip-- fma-udef distribute-lft-out--
1×cbrt-undiv pow-to-exp sub-neg frac-2neg diff-log rem-log-exp pow-exp associate--l+ clear-num log-pow
Counts
4 → 140
Calls
4 calls:
27.0ms
(- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y))
1.0ms
(fma (/ x (pow y 2)) 1.0 (/ x y))
18.0ms
(log (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y)))
8.0ms
(/ x (pow y 2))

series233.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y))
68.0ms
(fma (/ x (pow y 2)) 1.0 (/ x y))
86.0ms
(log (- (fma (/ x (pow y 2)) 1.0 (/ x y)) (/ 1.0 y)))
36.0ms
(/ x (pow y 2))

simplify1.7s

Counts
152 → 152
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02913965
16023614
215772882
done50012283

prune440.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes110.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 16.4b

bsearch1.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03068
13468
done3468

end0.0ms

sample2.7s

Algorithm
intervals
Results
619.0ms707×body640valid
468.0ms5751×body80valid
411.0ms825×body1280valid
326.0ms3739×body80nan
100.0ms351×body1280nan
90.0ms399×body640nan
84.0ms462×body320valid
61.0ms255×body160valid
33.0ms204×body320nan
11.0ms105×body160nan