Details

Time bar (total: 3.6s)

sample20.0ms

Algorithm
intervals
Results
10.0ms270×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: 26.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (* b c) (* a d))
25.9b
(/ (- (* 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)))

series124.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify108.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0268481
11010432
23840422
35001421

prune143.0ms

Filtered
56 candidates to 46 candidates (82.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 12.3b

localize12.0ms

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)))
0.5b
(- (* b c) (* a d))
16.0b
(/ (- (* 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)
12.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms
(- (* b c) (* a d))
9.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series378.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot c d)
178.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
41.0ms
(- (* b c) (* a d))
116.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify58.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05441126
12248931
25001929

prune306.0ms

Filtered
132 candidates to 91 candidates (68.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

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))
0.5b
(- (* b c) (* a d))
16.0b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite22.0ms

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)
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))

series317.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot c d)
116.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
39.0ms
(- (* b c) (* a d))
117.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify49.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04581435
116671331
250011322

prune373.0ms

Filtered
143 candidates to 112 candidates (78.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* a d) (hypot c d)) (hypot c d))
0.5b
(/ (/ (* b c) (hypot c d)) (hypot c d))
9.3b
(/ (* a d) (hypot c d))
12.0b
(/ (* b c) (hypot c d))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
16×associate-/l*
14×cbrt-undiv div-exp
12×associate-/r* div-inv
4×pow1 expm1-log1p-u frac-2neg prod-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 146
Calls
4 calls:
10.0ms
(/ (/ (* a d) (hypot c d)) (hypot c d))
6.0ms
(/ (/ (* b c) (hypot c d)) (hypot c d))
4.0ms
(/ (* a d) (hypot c d))
4.0ms
(/ (* b c) (hypot c d))

series281.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (/ (* a d) (hypot c d)) (hypot c d))
73.0ms
(/ (/ (* b c) (hypot c d)) (hypot c d))
71.0ms
(/ (* a d) (hypot c d))
65.0ms
(/ (* b c) (hypot c d))

simplify53.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04951158
121661010
25001996

prune419.0ms

Filtered
158 candidates to 114 candidates (72.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.9b

regimes215.0ms

Accuracy

52.8% (3.9b remaining)

Error of 4.5b against oracle of 0.6b and baseline of 8.9b

bsearch62.0ms

Steps
ItersRangePoint
5
34.599243829922614
136.14768989527596
132.18283498003242
7
-1.096686532935418e+141
-6.53821749653104e+138
-9.107098262182977e+139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04136
14736
24736

end0.0ms

sample512.0ms

Algorithm
intervals
Results
308.0ms8443×body80valid