Details

Time bar (total: 4.1s)

sample19.0ms

Algorithm
intervals
Results
9.0ms270×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
27.3b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
4.0ms
(+ (* c c) (* d d))
4.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series156.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
41.0ms
(- (* b c) (* a d))
88.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune193.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
16.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×prod-exp
26×add-cbrt-cube
25×add-sqr-sqrt
23×div-exp
22×times-frac
20×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×rec-exp
5×pow1 add-log-exp
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 110
Calls
3 calls:
12.0ms
(* (/ 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))

series333.0ms

Counts
3 → 9
Calls
3 calls:
179.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
40.0ms
(- (* b c) (* a d))
113.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify59.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05351099
12235907
25001905

prune263.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b
(- (* b c) (* a d))
16.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
7.0ms
(/ (/ (- (* 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))

series270.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms
(- (* b c) (* a d))
113.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04491408
116571307
250011298

prune336.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (hypot c d))) (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))))
0.3b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
0.5b
(- (* b c) (* a d))
16.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite80.0ms

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

series531.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (/ 1 (sqrt (hypot c d))) (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))))
200.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
40.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify70.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011895061
150024531

prune788.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.3b

regimes211.0ms

Accuracy

37.8% (8.4b remaining)

Error of 11.9b against oracle of 3.4b and baseline of 17.0b

bsearch141.0ms

Steps
ItersRangePoint
11
9.199612759357812e+156
8.1420769820787e+178
2.138099036698885e+168
9
-2.355035228211621e+66
-1.5442358469082974e+61
-4.1874568029823826e+61
9
-2.0967680061864643e+191
-1.139231286186639e+184
-2.0951350871904923e+187

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04931
15831
26131
36131

end0.0ms

sample474.0ms

Algorithm
intervals
Results
280.0ms8451×body80valid