Details

Time bar (total: 12.1s)

sample26.0ms

Algorithm
intervals
Results
10.0ms272×body80valid

simplify100.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01115
12114
24014
35614
47614
58814
69214
done9214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* b c) (* a d))
28.4b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite51.0ms

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-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
16.0ms
(- (* b c) (* a d))
32.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series171.0ms

Counts
2 → 6
Calls
2 calls:
61.0ms
(- (* b c) (* a d))
110.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.8s

Counts
56 → 56
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0961020
1269919
2928841
33207837
done5000836

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(hypot c d)
0.2b
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
18.7b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×times-frac
28×add-exp-log *-un-lft-identity
26×add-cube-cbrt
18×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×pow1 unswap-sqr
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×associate-/r* div-inv associate-/l*
2×rec-exp hypot-udef 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 107
Calls
4 calls:
0.0ms
(hypot c d)
0.0ms
(hypot c d)
42.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
6.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series595.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(hypot c d)
54.0ms
(hypot c d)
238.0ms
(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
243.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify3.2s

Counts
119 → 119
Iterations

Useful iterations: done (3.1s)

IterNodesCost
01422031
13391896
210631646
340201646
done50001612

prune350.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(hypot c d)
0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
18.7b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite24.0ms

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)
12.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
6.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series406.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
52.0ms
(hypot c d)
150.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
158.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify1.6s

Counts
133 → 133
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01632658
13332594
27072407
321692353
done50002289

prune456.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (fma b c (- (* d a))) (hypot c d)) (* (sqrt (hypot c d)) (sqrt (hypot c d))))
0.5b
(* (sqrt (hypot c d)) (sqrt (hypot c d)))
18.7b
(/ (fma b c (- (* d a))) (hypot c d))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
34×add-cube-cbrt *-un-lft-identity
20×add-exp-log add-cbrt-cube
19×pow1
18×sqrt-prod
16×associate-/l*
8×sqrt-pow1 pow1/2 swap-sqr
7×cbrt-undiv div-exp
6×associate-*r* associate-*l*
5×pow-prod-up
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv add-log-exp unswap-sqr
3×pow-prod-down prod-exp pow-sqr cbrt-unprod
2×frac-2neg clear-num
1×pow2 hypot-udef pow-plus sqrt-unprod rem-square-sqrt *-commutative associate-/l/
Counts
4 → 138
Calls
4 calls:
0.0ms
(hypot c d)
19.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (* (sqrt (hypot c d)) (sqrt (hypot c d))))
14.0ms
(* (sqrt (hypot c d)) (sqrt (hypot c d)))
6.0ms
(/ (fma b c (- (* d a))) (hypot c d))

series382.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(hypot c d)
145.0ms
(/ (/ (fma b c (- (* d a))) (hypot c d)) (* (sqrt (hypot c d)) (sqrt (hypot c d))))
46.0ms
(* (sqrt (hypot c d)) (sqrt (hypot c d)))
145.0ms
(/ (fma b c (- (* d a))) (hypot c d))

simplify1.2s

Counts
150 → 150
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01682664
13142028
211201769
done50001763

prune422.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 6.7b

regimes252.0ms

Accuracy

35.7% (7.3b remaining)

Error of 13.0b against oracle of 5.7b and baseline of 17.1b

bsearch66.0ms

Steps
ItersRangePoint
10
1.5037952905502068e+114
6.301337098361931e+125
7.666528689436016e+118
5
-2.5462563697763136e+164
-6.640649950346996e+163
-9.626862058130033e+163

simplify8.0ms

Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
02549
13640
23834
34234
done4234

end0.0ms

sample620.0ms

Algorithm
intervals
Results
298.0ms8509×body80valid