Details

Time bar (total: 9.7s)

sample40.0ms

Algorithm
intervals
Results
17.0ms265×body80valid

simplify81.0ms

Counts
1 → 1
Iterations
IterNodes
done94
694
590
476
356
240
121
011

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
1.4b
(- (* b c) (* a d))
29.3b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* log1p-expm1-u associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
3 → 64
Calls
3 calls:
12.0ms
(+ (* c c) (* d d))
10.0ms
(- (* b c) (* a d))
20.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series259.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (* c c) (* d d))
56.0ms
(- (* b c) (* a d))
166.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify975.0ms

Counts
73 → 73
Iterations
IterNodes
done5000
21783
1335
0110

prune431.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.3b
(* (/ 1 (hypot c d)) (/ (fma b c (* (- d) a)) (hypot c d)))
1.3b
(fma b c (* (- d) a))
18.1b
(/ (fma b c (* (- d) a)) (hypot c d))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative fma-udef pow-flip inv-pow
Counts
4 → 130
Calls
4 calls:
4.0ms
(/ 1 (hypot c d))
20.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (* (- d) a)) (hypot c d)))
0.0ms
(fma b c (* (- d) a))
8.0ms
(/ (fma b c (* (- d) a)) (hypot c d))

series553.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ 1 (hypot c d))
231.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (* (- d) a)) (hypot c d)))
55.0ms
(fma b c (* (- d) a))
197.0ms
(/ (fma b c (* (- d) a)) (hypot c d))

simplify1.3s

Counts
142 → 142
Iterations
IterNodes
done5001
22800
1410
0155

prune702.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (fma b c (* (- d) a)) (hypot c d)) (hypot c d))
1.3b
(fma b c (* (- d) a))
18.1b
(/ (fma b c (* (- d) a)) (hypot c d))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
16×associate-/l*
11×add-cbrt-cube add-exp-log
6×associate-/r* div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×hypot-udef fma-udef associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot c d)
10.0ms
(/ (/ (fma b c (* (- d) a)) (hypot c d)) (hypot c d))
0.0ms
(fma b c (* (- d) a))
4.0ms
(/ (fma b c (* (- d) a)) (hypot c d))

series415.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(hypot c d)
151.0ms
(/ (/ (fma b c (* (- d) a)) (hypot c d)) (hypot c d))
50.0ms
(fma b c (* (- d) a))
163.0ms
(/ (fma b c (* (- d) a)) (hypot c d))

simplify601.0ms

Counts
133 → 133
Iterations
IterNodes
done5000
21578
1357
0169

prune606.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot c d) (fma b c (- (* a d))))) (hypot c d))
0.2b
(/ 1 (/ (hypot c d) (fma b c (- (* a d)))))
1.3b
(fma b c (- (* a d)))
18.1b
(/ (hypot c d) (fma b c (- (* a d))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
36×add-exp-log
23×div-inv
22×div-exp
20×add-cbrt-cube
19×associate-/r*
10×cbrt-undiv
5×pow1 associate-/r/
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×fma-udef pow-flip inv-pow associate-/l/
Counts
4 → 319
Calls
4 calls:
19.0ms
(/ (/ 1 (/ (hypot c d) (fma b c (- (* a d))))) (hypot c d))
8.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* a d)))))
0.0ms
(fma b c (- (* a d)))
4.0ms
(/ (hypot c d) (fma b c (- (* a d))))

series484.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(/ (/ 1 (/ (hypot c d) (fma b c (- (* a d))))) (hypot c d))
133.0ms
(/ 1 (/ (hypot c d) (fma b c (- (* a d)))))
51.0ms
(fma b c (- (* a d)))
107.0ms
(/ (hypot c d) (fma b c (- (* a d))))

simplify614.0ms

Counts
331 → 331
Iterations
IterNodes
done5001
11322
0459

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

regimes366.0ms

Accuracy

36.3% (7.2b remaining)

Error of 13.3b against oracle of 6.1b and baseline of 17.4b

bsearch81.0ms

Steps
ItersRangePoint
8
9.289053748617585e+187
5.249487407627581e+192
1.884834830237687e+188
8
-4.078082968892708e+157
-8.099463720481524e+154
-1.656598338970387e+155

simplify7.0ms

Iterations
IterNodes
done48
348
246
136
024

end0.0ms

sample906.0ms

Algorithm
intervals
Results
556.0ms8523×body80valid