Details

Time bar (total: 4.1s)

sample29.0ms

Algorithm
intervals
Results
10.0ms282×body80valid
4.0ms104×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0227
1467
2727
3997
41207
51207

prune2.0ms

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: 23.1b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
5.3b
(* (* x y) z)
7.7b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.5b
(sqrt (- (* z z) (* t a)))

rewrite23.0ms

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×expm1-log1p-u sqrt-div log1p-expm1-u
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 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
4.0ms
(- (* z z) (* t a))
5.0ms
(* (* x y) z)
9.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms
(sqrt (- (* z z) (* t a)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(- (* z z) (* t a))
26.0ms
(* (* x y) z)
81.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
56.0ms
(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0368630
11941560
25001551

prune263.0ms

Filtered
98 candidates to 71 candidates (72.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New881098
Fresh000
Picked101
Done000
Total891099

Merged error: 3.8b

Counts
99 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ z (sqrt (- (* z z) (* t a))))
0.6b
(- (* z z) (* t a))
2.9b
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.5b
(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×expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
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 fma-neg diff-log associate-*r/ associate-*l* prod-diff clear-num *-commutative
Counts
4 → 122
Calls
4 calls:
6.0ms
(/ z (sqrt (- (* z z) (* t a))))
4.0ms
(- (* z z) (* t a))
15.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms
(sqrt (- (* z z) (* t a)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ z (sqrt (- (* z z) (* t a))))
36.0ms
(- (* z z) (* t a))
85.0ms
(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04531067
12239963
25001942

prune335.0ms

Filtered
134 candidates to 93 candidates (69.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1286134
Fresh549
Picked101
Done000
Total13410144

Merged error: 3.5b

Counts
144 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

3.3b
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
23.5b
(sqrt (- (* z z) (* t a)))
23.5b
(sqrt (- (* z z) (* t a)))
23.5b
(sqrt (- (* z z) (* t a)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
23×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
8×sqrt-div
7×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 86
Calls
4 calls:
6.0ms
(cbrt (/ z (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)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(cbrt (/ z (sqrt (- (* z z) (* t a)))))
60.0ms
(sqrt (- (* z z) (* t a)))
57.0ms
(sqrt (- (* z z) (* t a)))
235.0ms
(sqrt (- (* z z) (* t a)))

simplify110.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0286857
1859832
23232817
35001814

prune376.0ms

Filtered
98 candidates to 80 candidates (81.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New97198
Fresh189
Picked101
Done000
Total999108

Merged error: 3.5b

Counts
108 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(* y (/ z (sqrt (- (* z z) (* t a)))))
2.2b
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.5b
(sqrt (- (* z z) (* t a)))

rewrite32.0ms

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×expm1-log1p-u sqrt-div pow-prod-down log1p-expm1-u
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 fma-neg diff-log prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
4.0ms
(- (* 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)))

series232.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* z z) (* t a))
58.0ms
(* y (/ z (sqrt (- (* z z) (* t a)))))
81.0ms
(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
61.0ms
(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0425829
11848729
25001717

prune260.0ms

Filtered
114 candidates to 80 candidates (70.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1113114
Fresh358
Picked011
Done000
Total1149123

Merged error: 3.5b

Counts
123 → 9

regimes375.0ms

Accuracy

85.4% (2.8b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 22.5b

bsearch89.0ms

Steps
ItersRangePoint
7
6.918666222260054e+119
4.593077973303497e+121
1.950809667300859e+120
11
-1.5496828323658496e+171
-1.010047755036718e+149
-2.4435402411691344e+151

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02710
13310
23310

end0.0ms

sample781.0ms

Algorithm
intervals
Results
329.0ms8809×body80valid
105.0ms2969×body80nan