Details

Time bar (total: 20.7s)

sample126.0ms

Algorithm
intervals
Results
44.0ms384×body80nan
34.0ms379×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 4 (208.0ms)

IterNodesCost
02024
14023
29223
326523
493422
5433522
done500022

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
0.3b
(fma (- x 0.5) (log x) 0.91893853320467)
5.9b
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
22×add-sqr-sqrt
20×add-cube-cbrt
12×prod-diff
9×times-frac add-log-exp
6×add-exp-log add-cbrt-cube
5×distribute-lft-out
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
3×associate-/r* associate-/l*
2×diff-log fma-udef distribute-lft-out--
1×cbrt-undiv sub-neg flip3-- frac-2neg div-exp associate--l+ clear-num sum-log flip-- div-inv difference-of-squares
Counts
4 → 84
Calls
4 calls:
0.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
156.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
0.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
8.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

series678.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
181.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)) x)
329.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
116.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) x)

simplify834.0ms

Counts
96 → 96
Iterations

Useful iterations: done (829.0ms)

IterNodesCost
01782316
14072178
213601923
done50011766

prune435.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))) x)
0.3b
(fma (- x 0.5) (log x) 0.91893853320467)
2.6b
(/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))
3.7b
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))

rewrite868.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
177×*-un-lft-identity
166×add-sqr-sqrt
164×add-cube-cbrt
144×sqrt-prod
25×associate-/l*
12×prod-diff associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv add-log-exp
5×distribute-lft-out
4×pow1 cbrt-undiv expm1-log1p-u fma-neg div-exp log1p-expm1-u
2×frac-2neg diff-log clear-num distribute-lft-out--
1×sub-neg flip3-- associate--l+ sum-log flip-- fma-udef associate-/l/ difference-of-squares
Counts
4 → 263
Calls
4 calls:
816.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))) x)
0.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
18.0ms
(/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))
19.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))

series824.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))) x)
413.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
114.0ms
(/ (/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x)) (sqrt x))
115.0ms
(/ (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt x))

simplify1.8s

Counts
275 → 275
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03838621
19057794
234717343
done50007127

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
0.1b
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))) x)
0.3b
(fma (- x 0.5) (log x) 0.91893853320467)
6.1b
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×*-un-lft-identity
19×add-cube-cbrt
13×add-exp-log associate-*r*
11×times-frac
9×prod-diff add-cbrt-cube add-log-exp
6×pow1
4×expm1-log1p-u prod-exp log1p-expm1-u
3×fma-neg associate-*l* unswap-sqr
2×diff-log div-exp cbrt-unprod fma-udef
1×cbrt-undiv sub-neg rec-exp flip3-- 1-exp associate-*r/ pow-prod-down associate--l+ sum-log un-div-inv *-commutative flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 88
Calls
4 calls:
0.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
51.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))) x)
0.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
24.0ms
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

series722.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333)
185.0ms
(- (+ (fma (- x 0.5) (log x) 0.91893853320467) (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))) x)
380.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
116.0ms
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (/ 1 x))

simplify1.5s

Counts
100 → 100
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02022400
15002120
219741841
done50011711

prune518.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1 x))
0.3b
(fma (- x 0.5) (log x) 0.91893853320467)
2.7b
(* (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (/ 1 x))) (sqrt (/ 1 x)))
3.8b
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (/ 1 x)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-prod
41×add-sqr-sqrt
32×associate-*r*
31×times-frac
30×*-un-lft-identity
28×add-cube-cbrt
13×pow1
11×add-exp-log add-cbrt-cube
6×sqrt-div
4×expm1-log1p-u associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 div-inv
2×*-commutative
1×frac-times pow-flip pow1/2 associate-*l/ fma-udef inv-pow
Counts
4 → 113
Calls
4 calls:
4.0ms
(sqrt (/ 1 x))
0.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
88.0ms
(* (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (/ 1 x))) (sqrt (/ 1 x)))
49.0ms
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (/ 1 x)))

series672.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (/ 1 x))
390.0ms
(fma (- x 0.5) (log x) 0.91893853320467)
102.0ms
(* (* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (/ 1 x))) (sqrt (/ 1 x)))
144.0ms
(* (fma (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z 0.083333333333333) (sqrt (/ 1 x)))

simplify1.7s

Counts
125 → 125
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02262224
15411902
224511711
done50001655

prune705.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.2b

regimes322.0ms

Accuracy

90.1% (0.2b remaining)

Error of 4.2b against oracle of 3.9b and baseline of 6.4b

bsearch94.0ms

Steps
ItersRangePoint
7
79008453277590.77
2078498843398427.0
864747444454020.6

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03165
13565
done3565

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s11664×body80valid
1.7s11674×body80nan