Details

Time bar (total: 15.1s)

sample36.0ms

Algorithm
intervals
Results
17.0ms272×body80valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01115
11713
22113
done2113

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize36.0ms

Local error

Found 1 expressions with local error:

26.6b
(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
10.0ms
(/ (fma a c (* b d)) (fma c c (* d d)))

series142.0ms

Counts
1 → 3
Calls
1 calls:
142.0ms
(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.3s

Counts
32 → 32
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
058623
195614
2242534
3925534
44389534
done5000534

prune177.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(/ 1 (hypot c d))
0.2b
(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
16.9b
(/ (fma a c (* b d)) (hypot c d))

rewrite45.0ms

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×frac-2neg clear-num
1×frac-times hypot-udef pow-flip associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 130
Calls
4 calls:
0.0ms
(hypot c d)
6.0ms
(/ 1 (hypot c d))
29.0ms
(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
5.0ms
(/ (fma a c (* b d)) (hypot c d))

series596.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(hypot c d)
78.0ms
(/ 1 (hypot c d))
255.0ms
(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
196.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify2.7s

Counts
142 → 142
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01542150
14072041
228571741
done50011723

prune451.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(hypot c d)
0.0b
(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
16.9b
(/ (fma a c (* b d)) (hypot c d))

rewrite22.0ms

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
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×hypot-udef frac-2neg clear-num
1×associate-/l/
Counts
4 → 121
Calls
4 calls:
0.0ms
(hypot c d)
0.0ms
(hypot c d)
11.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
5.0ms
(/ (fma a c (* b d)) (hypot c d))

series487.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(hypot c d)
55.0ms
(hypot c d)
180.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
185.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify910.0ms

Counts
133 → 133
Iterations

Useful iterations: done (906.0ms)

IterNodesCost
01612502
13552439
216282270
done50012228

prune569.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (hypot c d))
0.0b
(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (hypot c d))
7.5b
(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
9.4b
(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
1644×times-frac
787×add-sqr-sqrt
786×add-cube-cbrt *-un-lft-identity
627×sqrt-prod
161×associate-/l*
38×div-inv
20×add-exp-log add-cbrt-cube
15×associate-/r*
10×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 799
Calls
4 calls:
2.0ms
(sqrt (hypot c d))
93.0ms
(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (hypot c d))
30.0ms
(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
7.0ms
(/ (fma a c (* b d)) (sqrt (hypot c d)))

series765.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(sqrt (hypot c d))
195.0ms
(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (hypot c d))
172.0ms
(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
278.0ms
(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify1.5s

Counts
811 → 811
Iterations

Useful iterations: done (1.5s)

IterNodesCost
084930067
1227027042
done500025823

prune2.5s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 5.1b

regimes346.0ms

Accuracy

36.6% (7.4b remaining)

Error of 13.0b against oracle of 5.7b and baseline of 17.3b

bsearch71.0ms

Steps
ItersRangePoint
7
1.5690019137202624e+163
2.5503030426441756e+164
1.907881629244538e+163
9
-1.115604885111551e+171
-1.0303680794832766e+166
-3.38269840734856e+168

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01833
12033
done2033

end0.0ms

sample1.0s

Algorithm
intervals
Results
645.0ms8446×body80valid