Details

Time bar (total: 3.5s)

sample20.0ms

Algorithm
intervals
Results
9.0ms276×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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.9b
(- (* b c) (* a d))
26.8b
(/ (- (* 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:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* c c) (* d d))
38.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify41.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune194.0ms

Filtered
73 candidates to 59 candidates (80.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.9b
(- (* b c) (* a d))
16.1b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite46.0ms

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))
26.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series381.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 1 (* (hypot c d) 1))
174.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
40.0ms
(- (* b c) (* a d))
116.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify61.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05531207
123041003
25001995

prune323.0ms

Filtered
155 candidates to 94 candidates (60.6%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.9b
(- (* b c) (* a d))
16.1b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite27.0ms

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:
10.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
9.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series265.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
38.0ms
(- (* b c) (* a d))
113.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify49.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04491408
116571307
250011298

prune353.0ms

Filtered
130 candidates to 99 candidates (76.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.1b
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
0.9b
(- (* b c) (* a d))
16.1b
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
29×add-sqr-sqrt
23×*-un-lft-identity times-frac
22×add-cube-cbrt
20×add-cbrt-cube
13×associate-*r*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l/ add-log-exp
5×flip3-- flip--
4×expm1-log1p-u frac-times associate-*l/ cbrt-unprod log1p-expm1-u associate-/l*
3×rec-exp 1-exp associate-*l* div-inv unswap-sqr
2×frac-2neg associate-*r/ clear-num un-div-inv
1×sub-neg pow-flip fma-neg diff-log prod-diff pow-prod-down *-commutative inv-pow
Counts
4 → 124
Calls
4 calls:
2.0ms
(/ 1 (hypot c d))
8.0ms
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
3.0ms
(- (* b c) (* a d))
15.0ms
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (hypot c d))
116.0ms
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
41.0ms
(- (* b c) (* a d))
114.0ms
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify53.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0417955
11964794
25002763

prune299.0ms

Filtered
136 candidates to 87 candidates (64.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.5b

regimes217.0ms

Accuracy

33.8% (8.1b remaining)

Error of 13.0b against oracle of 4.8b and baseline of 17.1b

bsearch70.0ms

Steps
ItersRangePoint
9
7.455959857371995e+127
1.7673157757263047e+135
9.145946385195369e+130
7
-1.6468005772374444e+103
-1.0948466605822108e+101
-1.5195216293899823e+103

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13115
23115

end0.0ms

sample504.0ms

Algorithm
intervals
Results
295.0ms8493×body80valid