Details

Time bar (total: 4.9s)

sample49.0ms

Algorithm
intervals
Results
31.0ms519×body80valid

simplify98.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 9 (82.0ms)

IterNodesCost
0216
1526
21716
34016
48296
510906
616106
719566
822526
923675
1023675

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.7b
(* (* y 4.0) (- (* z z) t))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×prod-diff
10×distribute-rgt-in distribute-lft-in associate--r+
8×add-sqr-sqrt
7×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
5×sub-neg
4×associate-*r* add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u
1×fma-neg diff-log associate-*l* *-commutative difference-of-squares
Counts
2 → 59
Calls
2 calls:
5.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
14.0ms
(* (* y 4.0) (- (* z z) t))

series153.0ms

Counts
2 → 6
Calls
2 calls:
81.0ms
(- (* x x) (* (* y 4.0) (- (* z z) t)))
71.0ms
(* (* y 4.0) (- (* z z) t))

simplify63.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0385490
11737408
25001399

prune157.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
2.5b
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
6.7b
(* (* y 4.0) (- (* z z) t))
6.7b
(* (* y 4.0) (- (* z z) t))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt *-un-lft-identity prod-diff
10×distribute-rgt-in distribute-lft-in
8×associate-*r*
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×expm1-log1p-u sub-neg flip3-- sqrt-div associate-*r/ flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative difference-of-squares
Counts
4 → 100
Calls
4 calls:
4.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
4.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
15.0ms
(* (* y 4.0) (- (* z z) t))
18.0ms
(* (* y 4.0) (- (* z z) t))

series445.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
158.0ms
(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
66.0ms
(* (* y 4.0) (- (* z z) t))
72.0ms
(* (* y 4.0) (- (* z z) t))

simplify55.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0352866
11571746
25001742

prune312.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y 4.0) (sqrt (- (* z z) t)))
0.2b
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
6.6b
(sqrt (- (* z z) t))
6.6b
(sqrt (- (* z z) t))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
18×add-exp-log sqrt-div add-cbrt-cube
16×add-sqr-sqrt sqrt-prod
14×associate-*r*
10×add-cube-cbrt *-un-lft-identity associate-*r/
9×flip3-- pow-prod-down prod-exp flip-- cbrt-unprod
4×expm1-log1p-u frac-times log1p-expm1-u add-log-exp difference-of-squares
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* associate-*l/ *-commutative
Counts
4 → 97
Calls
4 calls:
15.0ms
(* (* y 4.0) (sqrt (- (* z z) t)))
45.0ms
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
6.0ms
(sqrt (- (* z z) t))
10.0ms
(sqrt (- (* z z) t))

series256.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* y 4.0) (sqrt (- (* z z) t)))
73.0ms
(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
49.0ms
(sqrt (- (* z z) t))
54.0ms
(sqrt (- (* z z) t))

simplify61.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0390815
11824695
25002683

prune316.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
6.6b
(sqrt (- (* z z) t))
6.6b
(sqrt (- (* z z) t))
6.6b
(sqrt (- (* z z) t))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
30×flip3-- flip--
28×frac-times
26×associate-*r/
23×sqrt-prod
21×pow1
18×add-exp-log add-cbrt-cube
17×add-sqr-sqrt
14×associate-*l/
10×add-cube-cbrt *-un-lft-identity associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp difference-of-squares
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 113
Calls
4 calls:
166.0ms
(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
6.0ms
(sqrt (- (* z z) t))
6.0ms
(sqrt (- (* z z) t))
6.0ms
(sqrt (- (* z z) t))

series235.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
50.0ms
(sqrt (- (* z z) t))
56.0ms
(sqrt (- (* z z) t))
55.0ms
(sqrt (- (* z z) t))

simplify77.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
05251633
122131346
250011235

prune441.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 3.9b

regimes408.0ms

Accuracy

74.5% (0.9b remaining)

Error of 3.5b against oracle of 2.6b and baseline of 6.1b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02516
12516

end0.0ms

sample1.4s

Algorithm
intervals
Results
979.0ms15852×body80valid