Details

Time bar (total: 4.2s)

sample34.0ms

Algorithm
intervals
Results
13.0ms287×body80valid
4.0ms99×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1457
2677
3947
41157
51157

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.6b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
4.8b
(* (* x y) z)
10.1b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×sqrt-div
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*l* clear-num *-commutative div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
10.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series218.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(- (* z z) (* t a))
23.0ms
(* (* x y) z)
85.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
69.0ms
(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0343583
11850515
25003510

prune210.0ms

Filtered
88 candidates to 60 candidates (68.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New771188
Fresh000
Picked101
Done000
Total781189

Merged error: 3.5b

Counts
89 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
1.0b
(- (* z z) (* t a))
3.8b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
24×associate-*r* sqrt-prod
18×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-div prod-exp associate-/r* cbrt-unprod add-log-exp
4×flip3-- associate-/r/ flip--
3×cbrt-undiv div-exp pow-prod-down associate-/l*
2×div-inv
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ associate-*l* clear-num *-commutative
Counts
4 → 112
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
3.0ms
(- (* z z) (* t a))
13.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
7.0ms
(sqrt (- (* z z) (* t a)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
82.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04281014
12153912
25002894

prune249.0ms

Filtered
124 candidates to 80 candidates (64.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1222124
Fresh2810
Picked101
Done000
Total12510135

Merged error: 3.0b

Counts
135 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* z z) (* t a))
1.3b
(* y (/ z (sqrt (- (* z z) (* t a)))))
1.8b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
25×associate-*r*
20×add-cube-cbrt *-un-lft-identity times-frac
18×add-exp-log add-cbrt-cube
13×sqrt-prod
12×pow1
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
4×sqrt-div pow-prod-down
3×flip3-- associate-*r/ flip-- unswap-sqr
2×cbrt-undiv div-exp associate-/r/ *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-inv
Counts
4 → 92
Calls
4 calls:
3.0ms
(- (* z z) (* t a))
11.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* z z) (* t a))
53.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
83.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0400774
11768676
25001668

prune220.0ms

Filtered
104 candidates to 67 candidates (64.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1013104
Fresh099
Picked101
Done000
Total10212114

Merged error: 3.0b

Counts
114 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

7.3b
(* (/ y (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
24.8b
(sqrt (- (* z z) (* t a)))
24.8b
(sqrt (- (* z z) (* t a)))
24.8b
(sqrt (- (* z z) (* t a)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
40×times-frac
33×associate-*r*
28×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×cbrt-prod
20×sqrt-div sqrt-prod
18×add-cbrt-cube
15×associate-*l*
14×cbrt-div
10×flip3-- associate-/r/ flip--
9×pow1
8×prod-exp cbrt-unprod unswap-sqr
7×cbrt-undiv div-exp
5×frac-times
4×add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l/
2×div-inv
1×pow-prod-down *-commutative
Counts
4 → 125
Calls
4 calls:
29.0ms
(* (/ y (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))
4.0ms
(sqrt (- (* z z) (* t a)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (/ y (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))) (/ z (cbrt (sqrt (- (* z z) (* t a))))))
66.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))
66.0ms
(sqrt (- (* z z) (* t a)))

simplify80.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05972224
128881990
250011867

prune598.0ms

Filtered
137 candidates to 105 candidates (76.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1370137
Fresh01111
Picked011
Done000
Total13712149

Merged error: 3.0b

Counts
149 → 12

regimes508.0ms

Accuracy

80.8% (4.1b remaining)

Error of 7.2b against oracle of 3.1b and baseline of 24.3b

bsearch97.0ms

Steps
ItersRangePoint
6
1.1511387161602912e+62
6.555056238908478e+62
6.475540425151654e+62
9
-1.9981157720309622e+85
-1.8020745581007495e+76
-1.7674712377813788e+82

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03023
13623
23623

end0.0ms

sample933.0ms

Algorithm
intervals
Results
435.0ms8876×body80valid
136.0ms2952×body80nan

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