Details

Time bar (total: 4.6s)

sample23.0ms

Algorithm
intervals
Results
12.0ms271×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (* b c) (* a d))
26.9b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite13.0ms

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:
4.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series123.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(- (* b c) (* a d))
85.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify103.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0268481
11010432
23840422
35001421

prune150.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b
(- (* b c) (* a d))
17.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
32×prod-exp
27×add-cbrt-cube
26×add-sqr-sqrt
23×div-exp
22×times-frac
21×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×pow1 rec-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 120
Calls
4 calls:
1.0ms
(hypot c d)
16.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series378.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
179.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify61.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05441122
12247931
25003929

prune318.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.3b
(- (* b c) (* a d))
17.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

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)
8.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series321.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
115.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
38.0ms
(- (* b c) (* a d))
121.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04581435
116671331
250011322

prune405.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
0.3b
(- (* b c) (* a d))
0.3b
(* (/ 1 (sqrt (hypot c d))) (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))))
17.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
350×times-frac
261×add-sqr-sqrt
181×*-un-lft-identity
171×add-cube-cbrt
110×sqrt-prod
82×associate-*r*
50×add-exp-log
32×add-cbrt-cube
25×unswap-sqr
22×div-exp associate-*l*
17×div-inv
16×associate-/l*
13×cbrt-undiv
12×prod-exp
9×associate-/r*
6×pow1 cbrt-unprod add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×frac-times sub-neg fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative
Counts
4 → 324
Calls
4 calls:
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
4.0ms
(- (* b c) (* a d))
44.0ms
(* (/ 1 (sqrt (hypot c d))) (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))))
9.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series549.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
44.0ms
(- (* b c) (* a d))
180.0ms
(* (/ 1 (sqrt (hypot c d))) (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))))
118.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify66.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011895061
150024533

prune869.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.5b

regimes255.0ms

Accuracy

16.4% (9.9b remaining)

Error of 14.9b against oracle of 5.0b and baseline of 16.8b

bsearch198.0ms

Steps
ItersRangePoint
8
2.1643198323001914e+150
2.946747073993286e+153
1.9537314790331482e+152
9
5.205620924581097e-64
4.292417494179173e-57
5.2737837352095884e-64
8
2.4480199621176693e-81
3.8498438171014314e-78
3.8050518390474684e-78
9
-5.749378329514241e+85
-6.325617960473731e+78
-7.280462391920087e+83
9
-4.3302507567477494e+162
-4.9616708661001533e+154
-5.030681393622023e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04640
14840
24840

end0.0ms

sample522.0ms

Algorithm
intervals
Results
307.0ms8503×body80valid