Details

Time bar (total: 4.4s)

sample35.0ms

Algorithm
intervals
Results
23.0ms276×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: 26.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(- (* b c) (* a d))
26.5b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite18.0ms

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:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
11.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series153.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
38.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0314555
11341496
25001481

prune190.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(- (* b c) (* a d))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
15.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 1 (* (hypot c d) 1))
3.0ms
(- (* b c) (* a d))
25.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
8.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series394.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 1 (* (hypot c d) 1))
38.0ms
(- (* b c) (* a d))
184.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
117.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify62.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05531207
123041003
25001995

prune321.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize10.0ms

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) 1))
0.3b
(- (* b c) (* a d))
15.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
6×add-log-exp
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv
3×div-sub associate-/l/
2×flip3-- frac-2neg 1-exp clear-num flip-- cbrt-unprod
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 109
Calls
4 calls:
0.0ms
(hypot c d)
10.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series324.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot c d)
117.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
43.0ms
(- (* b c) (* a d))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify48.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0430989
11703876
25001875

prune323.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b c) (* a d))
0.3b
(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b
(* (sqrt (/ 1 (* (hypot c d) 1))) (* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d))))
15.8b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
26×times-frac
25×add-cube-cbrt *-un-lft-identity
20×add-exp-log associate-*l* add-cbrt-cube
16×sqrt-prod
14×associate-*r*
11×pow1
10×sqrt-div
7×prod-exp cbrt-unprod
6×frac-times associate-*r/ add-log-exp
4×expm1-log1p-u pow-prod-down associate-*l/ log1p-expm1-u div-inv unswap-sqr
3×cbrt-undiv div-exp associate-/r* associate-/l*
2×flip3-- *-commutative flip-- associate-/l/
1×sub-neg frac-2neg fma-neg diff-log div-sub prod-diff clear-num
Counts
4 → 129
Calls
4 calls:
3.0ms
(- (* b c) (* a d))
27.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d)))
63.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d))))
8.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series606.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b c) (* a d))
263.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d)))
182.0ms
(* (sqrt (/ 1 (* (hypot c d) 1))) (* (sqrt (/ 1 (* (hypot c d) 1))) (/ (- (* b c) (* a d)) (hypot c d))))
118.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify81.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05251554
126651314
250011267

prune406.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.6b

regimes238.0ms

Accuracy

32.2% (8.1b remaining)

Error of 12.6b against oracle of 4.5b and baseline of 16.5b

bsearch76.0ms

Steps
ItersRangePoint
6
2.702607740933448e+197
1.1619739797922657e+198
3.26314722618804e+197
8
-6.216769361477498e+182
-9.641701532767943e+179
-2.235279546431987e+180

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13215
23215

end0.0ms

sample866.0ms

Algorithm
intervals
Results
644.0ms8445×body80valid