Details

Time bar (total: 31.8s)

sample45.0ms

Algorithm
intervals
Results
22.0ms262×body80valid

simplify103.0ms

Counts
1 → 1
Iterations
IterNodes
done80
580
476
356
240
121
011

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* c b) (* d a))
25.9b
(/ (- (* c b) (* d a)) (fma d d (* c c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num div-inv
Counts
2 → 48
Calls
2 calls:
19.0ms
(- (* c b) (* d a))
42.0ms
(/ (- (* c b) (* d a)) (fma d d (* c c)))

series261.0ms

Counts
2 → 6
Calls
2 calls:
88.0ms
(- (* c b) (* d a))
173.0ms
(/ (- (* c b) (* d a)) (fma d d (* c c)))

simplify6.7s

Counts
54 → 54
Iterations
IterNodes
done5001
32575
2741
1222
088

prune726.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* c b) (* d a)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
16.4b
(/ (- (* c b) (* d a)) (sqrt (fma d d (* c c))))
28.8b
(sqrt (fma d d (* c c)))
28.8b
(sqrt (fma d d (* c c)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×add-cube-cbrt *-un-lft-identity
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num fma-udef hypot-def
1×flip3-- flip--
Counts
4 → 254
Calls
4 calls:
174.0ms
(/ (/ (- (* c b) (* d a)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
42.0ms
(/ (- (* c b) (* d a)) (sqrt (fma d d (* c c))))
4.0ms
(sqrt (fma d d (* c c)))
4.0ms
(sqrt (fma d d (* c c)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (/ (- (* c b) (* d a)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
208.0ms
(/ (- (* c b) (* d a)) (sqrt (fma d d (* c c))))
85.0ms
(sqrt (fma d d (* c c)))
86.0ms
(sqrt (fma d d (* c c)))

simplify3.2s

Counts
266 → 266
Iterations
IterNodes
done5000
21746
1646
0273

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.2b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* c b) (* a d))
0.2b
(* (/ (hypot c d) (- (* c b) (* a d))) (hypot c d))
0.9b
(/ 1 (* (/ (hypot c d) (- (* c b) (* a d))) (hypot c d)))
16.5b
(/ (hypot c d) (- (* c b) (* a d)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity times-frac
20×add-cbrt-cube
15×associate-*l*
11×div-exp
9×pow1
8×prod-exp
6×cbrt-undiv associate-/l* add-log-exp
5×associate-/r/
4×expm1-log1p-u associate-/r* cbrt-unprod log1p-expm1-u
3×rec-exp flip3-- 1-exp associate-*r* flip-- div-inv
2×pow-flip frac-2neg pow-prod-down associate-*l/ clear-num unswap-sqr
1×sub-neg fma-neg diff-log prod-diff *-commutative inv-pow
Counts
4 → 118
Calls
4 calls:
17.0ms
(- (* c b) (* a d))
63.0ms
(* (/ (hypot c d) (- (* c b) (* a d))) (hypot c d))
58.0ms
(/ 1 (* (/ (hypot c d) (- (* c b) (* a d))) (hypot c d)))
29.0ms
(/ (hypot c d) (- (* c b) (* a d)))

series788.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (* c b) (* a d))
195.0ms
(* (/ (hypot c d) (- (* c b) (* a d))) (hypot c d))
341.0ms
(/ 1 (* (/ (hypot c d) (- (* c b) (* a d))) (hypot c d)))
170.0ms
(/ (hypot c d) (- (* c b) (* a d)))

simplify6.4s

Counts
130 → 130
Iterations
IterNodes
done5000
34758
21468
1404
0157

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(- (* b c) (* a d))
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
16.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
1.0ms
(hypot c d)
18.0ms
(- (* b c) (* a d))
51.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
40.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series690.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(hypot c d)
86.0ms
(- (* b c) (* a d))
260.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
250.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify2.7s

Counts
143 → 143
Iterations
IterNodes
done5001
21447
1468
0193

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

regimes667.0ms

Accuracy

35.8% (7.1b remaining)

Error of 12.7b against oracle of 5.6b and baseline of 16.7b

bsearch153.0ms

Steps
ItersRangePoint
8
5.940403946604681e+112
8.52917001719722e+115
4.7901533884695995e+114
7
-2.969531820227428e+117
-1.73563149561513e+115
-5.589725284818602e+116

simplify7.0ms

Iterations
IterNodes
done23
123
020

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.4s8466×body80valid