Details

Time bar (total: 5.3s)

sample20.0ms

Algorithm
intervals
Results
9.0ms268×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.8b
(- (* b c) (* a d))
26.9b
(/ (- (* 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)))

series159.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* c c) (* d d))
42.0ms
(- (* b c) (* a d))
90.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0314555
11341496
25001481

prune192.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 12.6b

localize14.0ms

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)))
0.8b
(- (* b c) (* a d))
16.0b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite44.0ms

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))
24.0ms
(* (/ 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))

series391.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (* (hypot c d) 1))
179.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
41.0ms
(- (* b c) (* a d))
117.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05531207
123041003
25001995

prune327.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

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))
0.8b
(- (* b c) (* a d))
16.0b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite24.0ms

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:
0.0ms
(hypot c d)
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series328.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(hypot c d)
118.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
43.0ms
(- (* b c) (* a d))
118.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify53.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04581435
116671331
250011322

prune367.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize16.0ms

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)) (hypot c d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
0.8b
(- (* b c) (* a d))
16.0b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
1566×times-frac
738×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
564×sqrt-prod
98×associate-/l*
59×div-inv
20×add-exp-log add-cbrt-cube
15×associate-/r*
10×cbrt-undiv div-exp
6×div-sub add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×frac-2neg clear-num
2×flip3-- flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 763
Calls
4 calls:
11.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
35.0ms
(/ (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series503.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d)))
120.0ms
(/ (/ (/ (- (* b c) (* a d)) (hypot c d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
38.0ms
(- (* b c) (* a d))
124.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify162.0ms

Algorithm
egg-herbie
Counts
775 → 775
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0195716693
1500115325

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

regimes228.0ms

Accuracy

31.9% (9.0b remaining)

Error of 12.6b against oracle of 3.6b and baseline of 16.8b

bsearch158.0ms

Steps
ItersRangePoint
10
2.7020643455585323e+180
2.94630534130054e+190
1.4538292767703705e+189
10
1.8137782181329498e-137
8.569503808472031e-128
6.17656804791985e-128
7
-2.85855713936286e-142
-2.3598379269180502e-144
-1.2987370292207596e-142
7
-9.149408721955617e+132
-1.9322020034710515e+131
-5.392764808821395e+132

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04635
14735
24735

end0.0ms

sample506.0ms

Algorithm
intervals
Results
291.0ms8469×body80valid